SCMA دانشگاه مراغه Sahand Communications in Mathematical Analysis 2322-5807 دانشگاه مراغه 37371 10.22130/scma.2019.93964.499 Research Paper A New Iterative Algorithm for Multivalued Nonexpansive Mappping and Equlibruim Problems with Applications A New Iterative Algorithm for Multivalued Nonexpansive Mappping and Equlibruim Problems with Applications Sow Thierno Mohadamane Mansour Gaston Berger University, Saint Louis, Senegal. 01 06 2020 17 2 1 22 17 09 2018 02 12 2019 Copyright © 2020, دانشگاه مراغه. 2020 https://scma.maragheh.ac.ir/article_37371.html

In this paper, we introduce two iterative schemes by a modified Krasnoselskii-Mann algorithm for finding a common element of the set of solutions of equilibrium problems and the set of fixed points of multivalued nonexpansive mappings in Hilbert space. We prove that the sequence generated by the proposed method converges strongly to a common element of the set of solutions of equilibruim problems and the set of fixed points of multivalued nonexpansive mappings which is also the minimum-norm element of the above two sets. Finally, some applications of our results to optimization problems with constraint and the split feasibility problem are given. No compactness assumption is made. The methods in the paper are novel and different from those in early and recent literature.

Multivalued mappings Equilibrium problems Iterative methods Applications
 E. Blum and W. Oettli, From optimization and variational inequalities to equilibrium problems, Math. Student, 63 (1994), pp. 123-145.  C. Bryne, Iterative oblique projection onto convex set and the split feasiblity problem, Inverse Problems, 18 (2002), pp. 441-453.  J. Caristi, Fixed points theorems and selections of set-valued contraction, J. Math. Anal., 227 (1988), pp. 55-67.  Y. Censor and T. Elfving, A multiprojection algorithm using Bregman projections in a product space, Numerical Algorithms, 8 (1994), pp. 221-239.  S. Chang, Y.Tang, L. Wang, Y. Xu, Y. Zhao, and G. Wang, Convergence theorems for some multivalued generalized nonexpansive mappings, Fixed Point Theory Appl., 33 (2014), pp. 1-11.  C.E. Chidume, Geometric Properties of Banach spaces and Nonlinear Iterations, Springer Verlag, 2009.  C.E. Chidume, C.O. Chidume, N. Djitte, and M. S. Minjibir, Convergence Theorems for Fixed Points of Multivalued Strictly Pseudocontractive Mappings in Hilbert Spaces, Abstract and Applied Analysis, 2013 (2013), pp. 1-10.  D. Downing and W.A. Kirk, Fixed point theorems for set-valued mappings in metric and Banach spaces, Mathematica Japonica, 22 (1977), pp. 99-112.  K. Fan, A minimax inequality and applications, in Inequalities III, (O. Shisha, ed.), Academic Press, New York, 1972.  Q-W. Fan and Z. Yao, Strong convergence theorems for nonexpansive mapping and its applications for solving the split feasibility problem, J. Nonlinear. Sci. App., 10 (2017), pp. 1470-1477.  J. Geanakoplos, Nash and Walras equilibrium via Brouwer, Economic Theory, 21 (2003), pp. 585-603.  L. Gorniewicz, Topological Fixed Point Theory of Multivalued Mappings, Dordrecht: Springer, 1999.  S. Kakutani, A generalization of Brouwer’s fixed point theorem, Duke Mathematical Journal, 8 (1941), pp. 457-459.  T.C. Lim and H.K. Xu, Fixed point theorems for assymptoticaly nonexpansive mapping, Nonlinear Analysis: Theory, Methods & Applications, 22 (1994), pp. 1345-1355.  J.T. Markin, Continuous dependence of fixed point sets, Proc. Am. Math. Soc., 38 (1973), pp. 545-547.  Jr. S. B. Nadler, Multivalued contraction mappings, Pacific J. Math., 30 (1969), pp. 475-488.  J.F. Nash, Equilibrium points in \$n\$-person games, Proceedings of the National Academy of Sciences of the United States of America, 36 (1950), pp. 48-49.  J.F. Nash, Non-coperative games, Annals of Mathematics, Second series, 54 (1951), pp. 286-295.  B. Panyanak, Mann and Ishikawa iteration processes for multivalued mappings in Banach Spaces, Comput. Math. Appl. 54 (2007), pp. 872-877.  N. Petrot, K. Wattanawitoon, and P. Kumam, A hybrid projection method for generalized mixed equilibrium problems and fixed point problems in Banach spaces, Nonlinear Analysis. Hybrid Systems, 4 (2010), pp 631-643.  X. Qin, S.Y. Cho, and S.M. Kang, Convergence of an iterative algorithm for systems of variational inequalities and nonexpansive mappings with applications, Journal of Computational and Applied Mathematics, 233 (2009), pp 231-240.  X. Qin, Y.J. Cho, S.M. Kang, and H. Zhou, Convergence of a modified Halpern-type iteration algorithm for quasi-\$phi\$-nonexpansive mappings, Applied Mathematics Letters, 22 (2009), pp. 1051-1055.  T.M.M. Sow, N. Djitte, and C.E. Chidume, A path convergence theorem and construction of fixed points for nonexpansive mappings in certain Banach spaces, Carpathian J.Math, 32 (2016), pp. 217-226.  S. Shoham, Iterative methods for solving optimization problems, Technion-Isreal Institute of Technology, Haifa, 2012.  H.K. Xu, A variable Krasnoselskii-Mann algorithm and the multiple set split feasiblity problem, Inverse Problem, 26 (2006), pp. 2021-2034.  H.K. Xu, Iterative algorithms for nonlinear operators, J. London Math. Soc., 66 (2002), pp. 240-256.  H.K. Xu, Iterative methods for the split feasiblity problem in infinite-dimensional Hilbert spaces, Inverse Problem, 26 (2010), pp. 1-17.
SCMA دانشگاه مراغه Sahand Communications in Mathematical Analysis 2322-5807 دانشگاه مراغه 37373 10.22130/scma.2019.97961.527 Research Paper Fixed Point Theorems on Complete Quasi Metric Spaces Via C-class and A-Class Functions Fixed Point Theorems on Complete Quasi Metric Spaces Via C-class and A-Class Functions Yalcin Mensur Department of Mathematics, Faculty of Science and Arts, Kirikkale University, 71450 Yahsihan, Kirikkale, Turkey. Simsek Hakan Department of Mathematics, Faculty of Science and Arts, Kirikkale University, 71450 Yahsihan, Kirikkale, Turkey. Altun Ishak Department of Mathematics, Faculty of Science and Arts, Kirikkale University, 71450 Yahsihan, Kirikkale, Turkey. 01 06 2020 17 2 23 36 19 11 2018 02 12 2019 Copyright © 2020, دانشگاه مراغه. 2020 https://scma.maragheh.ac.ir/article_37373.html

In this paper, we present some fixed point theorems for single valued mappings on \$K\$-complete, \$M\$-complete and Symth complete quasi metric spaces. Here, for contractive condition, we consider some altering distance functions together with functions belonging to \$C\$-class and \$A\$-class. At the same time, we will consider two different type \$M\$ functions in contractive conditions because the quasi metric does not provide the symmetry property. Finally, we show that our main results includes many fixed point theorems presented on both complete metric and complete quasi metric spaces in the literature. We also provide an illustrative example to show importance of our results.

Quasi metric space left \$K\$-Cauchy sequence left \$mathcal{K}\$-completeness Fixed point
SCMA دانشگاه مراغه Sahand Communications in Mathematical Analysis 2322-5807 دانشگاه مراغه 37410 10.22130/scma.2018.86797.440 Research Paper Some Fixed Point Theorems in Generalized Metric Spaces Endowed with Vector-valued Metrics and Application in Linear and Nonlinear Matrix Equations Some Fixed Point Theorems in Generalized Metric Spaces Endowed with Vector-valued Metrics and Application in Linear and Nonlinear Matrix Equations Hosseinzadeh Hasan Department of Mathematics, Ardabil Branch, Islamic Azad University, Ardabil, Iran. 01 06 2020 17 2 37 53 24 05 2018 07 12 2019 Copyright © 2020, دانشگاه مراغه. 2020 https://scma.maragheh.ac.ir/article_37410.html

Let \$mathcal{X}\$ be a partially ordered set and \$d\$ be a generalized metric on \$mathcal{X}\$. We obtain some results in coupled and coupled coincidence of \$g\$-monotone functions on \$mathcal{X}\$, where \$g\$ is a function from \$mathcal{X}\$ into itself. Moreover, we show that a nonexpansive mapping on a partially ordered Hilbert space has a fixed point lying in  the unit ball of  the Hilbert space. Some applications for linear and nonlinear matrix equations are given.

Fixed points Coupled fixed point Coupled coincidence fixed Point Generalized metric
 G. Allaire and S. M. Kaber, Numerical linear algebra, Vol. 55 of Texts in Applied Mathematics, Springer-New York, 2008.  T. Gnana Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65(2006),pp. 1379-1393.  A. D. Filip and Petrusel, Fixed point theorems on spaces endowed with vector-valued metrics, Fixed Point Theory and Applications, 20 (2010).  H. Hosseinzadeh, A. Jabbari and A. Razani, Fixed point and common fixed point theorems on spaces which endowed vector-valued metrics, Ukrainian J. Math., 65 (50)(2013), pp. 814-822.  R. Precup, The role of matrices that are convergent to zero in the study of semilinear operator systems, Mathematical and Computer Modelling, 49(3-4) (2009), pp. 703-708.  A. C. M. Ran and M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132(5) (2003), pp. 1435-1443.  A. Razani, H. Hosseinzadeh and A. Jabbari, Coupled fixed point theorems in partially ordered metric spaces which endowed vector-valued metrics, Aust. J. Basic and App. Sci., 6(2)(2012),pp. 124-129.  B. Ricceri, Another fixed point theorem for nonexpansive potential operators, Studia Math., 211(2)(2012), pp. 147-151.  I. A. Rus, Principles and applications of the fixed point theory, Dacia, Cluj-Napoca, Romania, 1979.  R. S. Varga, Matrix iterative analysis, Vol. 27 of Springer Series in Computational Mathematics, Springer-Berlin, 2000.
SCMA دانشگاه مراغه Sahand Communications in Mathematical Analysis 2322-5807 دانشگاه مراغه 37411 10.22130/scma.2018.88329.461 Research Paper Some Results on the Field of Values of Matrix Polynomials Some Results on the Field of Values of Matrix Polynomials Boor Boor Azimi Zahra Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran. Aghamollaei Gholamreza Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran. 01 06 2020 17 2 55 68 18 06 2018 16 11 2019 Copyright © 2020, دانشگاه مراغه. 2020 https://scma.maragheh.ac.ir/article_37411.html

In this paper, the notions of pseudofield of values and joint pseudofield of values of matrix polynomials are introduced and some of their algebraic and geometrical properties are studied.  Moreover, the relationship between the pseudofield of values of a matrix polynomial and the pseudofield of values of its companion linearization is stated, and then some properties of the augmented field of values of basic A-factor block circulant matrices are investigated.

‎Field of values Perturbation Matrix polynomial companion linearization Basic \$A-\$factor block circulant matrix
 Gh. Aghamollaei and A. Salemi, Polynomial numerical hulls of matrix polynomials, II, Linear Multilinear Algebra, 59 (2011), pp. 291-302.  J.C.R. Claeyssen and L.A.S. Leal, Diagonalization and spectral decomposition of factor block circulant matrices, Linear Algebra Appl., 99 (1988), pp. 41-61.  M. Eiermann, Field of values and iterative methods, Linear Algebra Appl., 180 (1993), pp. 167-197.  I. Gohberg, P. Lancaster and L. Rodman, Matrix Polynomials, Academic Press, New York, 1982.  K.E. Gustafson and D.K.M. Rao, Numerical Range: The Field of values of Linear Operators and Matrices, Springer-Verlage, New York, 1997.  R.A. Horn and Ch. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991.  M. Khakshour, Gh. Aghamollaei, and A. Sheikhhosseini, Field of values of perturbed matrices and quantum states, Turkish J. Math., 42 (2018), pp. 647-655.  C.K. Li and L. Rodman, Numerical range of matrix polynomials, SIAM J. Matrix Anal. Appl., 15 (1994), pp. 1256-1265.  F. Tisseur and N.J. Higham, Structured pseudospectra for polynomial eigenvalue problems with applications, SIAM J. Matrix Anal. Appl., 23 (2001), pp. 187-208.  L.N. Trefethen and M. Embree, Spectra and Pseudospectra, The Bihavior of Nonnormal Matrices and Operators, Princeton University Press, Princeton, 2005.
SCMA دانشگاه مراغه Sahand Communications in Mathematical Analysis 2322-5807 دانشگاه مراغه 37712 10.22130/scma.2018.85895.433 Research Paper Vector Optimization Problems and Generalized Vector Variational-Like Inequalities Vector Optimization Problems and Generalized Vector Variational-Like Inequalities Sadeqi Ildar Department of Mathematics, Sahand University of Technology, Tabriz, Iran. Nadi Somayeh Department of Mathematics, Sahand University of Technology, Tabriz, Iran. 01 06 2020 17 2 69 82 10 05 2018 18 12 2019 Copyright © 2020, دانشگاه مراغه. 2020 https://scma.maragheh.ac.ir/article_37712.html

In this paper, some properties of  pseudoinvex functions, defined by means of  limiting subdifferential, are discussed. Furthermore, the Minty vector variational-like inequality,  the Stampacchia vector variational-like inequality, and the  weak formulations of these two inequalities  defined by means of limiting subdifferential are studied. Moreover, some relationships  between the vector variational-like inequalities and vector optimization problems are established.

Nonsmooth functions Limiting subdifferential Pseudoinvex functions Vector variational-like inequalities Vector optimization problems
 S. Al-Homidan and Q.H. Ansari, Generalized Minty vector variational-like inequalities and vector optimization problems, J. Optim. Theory Appl., 144 (2010), pp. 1-11.  Q.H. Ansari and M. Rezaei, Generalized vector variational-like inequalities and vector optimization in Asplund spaces, Optimization, 62 (2013), pp. 721-734.  Q.H. Ansari, S. Schaible, and J.-C. Yao, it \$eta\$-Pseudolinearity, Riviste Mat. Sci. Econ. Soc., 22 (1999), pp. 31-39.  Q.H. Ansari and J.-C. Yao (eds.), Recent Developments in Vector Optimization, Springer-Verlag, Berlin, New York, Heidelberg, 2012.  B. Chen and N.-J. Huang, Vector variational-like inequalities and vector optimization problems in Asplund spaces, Optim. Lett., 6 (2012), pp. 1513-1525 .  A. Chinchuluun, P.M. Pardalos, A. Migdalas, and L. Pitsoulis, Pareto Optimality, Game Theory and Equilibria, Springer-Verlag, New York, 2008.  F. Giannessi, On Minty variational principle, in New Trends in Mathematical Programming, F. Giannessi, S. Komloski, and T. Tapcsack, eds., Kluwer Academic Publisher, Dordrecht, Holland, 1998, pp. 93-99.  F. Giannessi, Theorems of alternative, quadratic programs and complementarity problems, In: R. W. Cottle, F. Giannessi, and J.-L. Lions, (eds.) Variational Inequalities and Complementarity Problems, Wiley, New York, 1980, pp. 151-186.  F. Giannessi, A. Maugeri, and P.M. Pardalos (eds.), Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models, Series: Nonconvex Optimizatin and Its Applications, Vo1. 58, Springer-Verlag, New York, 2002.  T. Jabarootian and J. Zafarani, Generalized invariant monotonicity and invexity of nondifferentiable functions, J. Global Optim., 36 (2006), pp. 537-564.  J. Jahn, Vector Optimization: Theory, Applications and Extensions, Springer-Verlage, Berlin, Heidelberg, New York, 2004.  S.R. Mohan and S.K. Neogy, On Invex sets and preinvex functions, J. Math. Anal. Appl., 189 (1995), pp. 901-908.  B.S. Mordukhovich, Variational analysis and generalized differentiation, I: Basic Theory, II: Applications, Springer, Berlin, 2006.  M. Oveisiha and J. Zafarani, Generalized Minty vector variational-like inequalities and vector optimization problems in Asplund spaces, Optim. Lett., 7 (2013), pp. 709-721.  M. Oveisiha and J. Zafarani, Vector optimization problem and generalized convexity, J. Optim. Theory App., 52 (2012), pp. 29-43.  M. Rezaie and J. Zafarani, Vector optimization and variational-like inequalities, J. Global Optim., 43 (2009), pp. 47-66.  M. Soleimani-damaneh, An optimization modelling for string selection in molecular biology using Pareto optimality, Appl. Math. Model., 35 (2011), pp. 3887-3892.  M. Soleimani-damaneh, Characterizations and applications of generalized invexity and monotonicity in Asplund spaces, Top., 18 (2010), pp. 1-22.  X.M. Yang and X.Q. Yang, Vector variational-like inequality with pseudoinvexity, Optimization, 55 (2006), pp. 157-170.  X.M. Yang, X.Q. Yang, and K. L. Teo, Generalized invexity and generalized invariant monotonicity, J. Optim. Theory Appl., 117 (2003), pp. 607-625.  X.M. Yang, X.Q. Yang, and K.L. Teo, Some remarks on the Minty vector variational inequality, J. Optim. Theory Appl., 121 (2004), pp. 193-201.
SCMA دانشگاه مراغه Sahand Communications in Mathematical Analysis 2322-5807 دانشگاه مراغه 37412 10.22130/scma.2018.92986.488 Research Paper Common Fixed Point Results on Complex-Valued \$S\$-Metric Spaces Common Fixed Point Results on Complex-Valued \$S\$-Metric Spaces Taş Nihal Department of Mathematics, Bali kesir University, 10145, Bali kesir, Turkey. Yilmaz Ozgur Nihal Department of Mathematics, Bal\i kesir University, 10145 Bal\i kesir, Turkey. 01 06 2020 17 2 83 105 03 09 2018 16 11 2019 Copyright © 2020, دانشگاه مراغه. 2020 https://scma.maragheh.ac.ir/article_37412.html

Banach's contraction principle has been improved and extensively studied on several generalized metric spaces. Recently, complex-valued \$S\$-metric spaces have been introduced and studied for this purpose. In this paper, we investigate some generalized fixed point results on a complete complex valued \$S\$-metric space. To do this, we prove some common fixed point (resp. fixed point) theorems using different techniques by means of new generalized contractive conditions and the notion of the closed ball. Our results generalize and improve some known fixed point results. We provide some illustrative examples to show the validity of our definitions and fixedpoint theorems.

\$S\$-metric space Fixed point theorem Common fixed point theorem Complex valued \$S\$-metric space
 J. Ahmad, A. Azam, and S. Saejung, Common fixed point results for contractive mappings in complex-valued metric spaces, Fixed Point Theory Appl., 67 (2014), 11 pp.  A.H. Ansari, O. Ege, and S. Radenovic, Some fixed point results on complex-valued \$G_b\$-metric spaces, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM, 112 (2018), pp. 463-472.  A.H. Ansari, T. Dosenovic, S. Radenovic, and J.S. Ume, \$C\$-class functions and common fixed point theorems satisfying \$varphi \$-weakly contractive conditions, Sahand Commun. Math. Anal.,(13) (2019), pp. 17-30.  A.H. Ansari and A. Razani, Some fixed point theorems for \$C\$-class functions in \$b\$-metric spaces, Sahand Commun. Math. Anal., 10 (2018), pp. 85-96.  A. Azam, B. Fisher, and M. Khan, Common fixed point theorems in complex-valued metric spaces, Numer. Funct. Anal. Optim., 32 (2011), pp. 243-253.  N.H. Dien, Some remarks on common fixed point theorems, J. Math. Anal. Appl., 187 (1994), pp. 76-90.  O. Ege, Complex valued rectangular \$b\$-metric spaces and an application to linear equations, J. Nonlinear Sci. Appl., 8 (2015), pp. 1014-1021.  O. Ege, Complex valued \$G_b\$-metric spaces, J. Comput. Anal. Appl., 21 (2016), pp. 363-368.  O. Ege, Some fixed point theorems in complex-valued \$G_b\$-metric spaces, J. Nonlinear Convex Anal., 18 (2017), pp. 1997-2005.  H. Faraji and K. Nourouzi, Fixed and common fixed points for \$(psi,varphi)\$-weakly contractive mappings in \$b\$-metric spaces, Sahand Commun. Math. Anal., 7 (2017), pp. 49-62.  C. Kalaivani and G. Kalpana, Fixed point theorems in \$C^ast \$-algebra-valued \$S\$-metric spaces with some applications, Sci. Bull., Ser. A, Appl. Math. Phys., Politeh. Univ. Buchar., 80 (2018), pp. 93-102.  Z. Liu, Y. Xu, and Y.J. Cho, On Characterizations of Ffixed and common fixed points, J. Math. Anal. Appl., 222 (1998), pp. 494-504.  N.M. Mlaiki, Common fixed points in complex \$S\$-metric space, Adv. Fixed Point Theory, 4 (2014), pp. 509-524.  N. Mlaiki, U. Celik, N. Tas, N.Y. Ozgur, and A. Mukheimer, Wardowski type contractions and the fixed-circle problem on \$S\$-metric spaces, J. Math., 2018 (2018), 9 pp.  N.Y. Ozgur and N. Tas, Some fixed point theorems on \$S\$-metric spaces, Mat. Vesnik, 69 (2017), pp. 39-52.  N.Y. Ozgur and N. Tas, Some new contractive mappings on \$S\$-metric spaces and their relationships with the mapping \$(S25)\$, Math. Sci., 11 (2017), pp. 7-16.  N.Y. Ozgur and N. Tas, Some generalizations of fixed point theorems on \$S\$-metric spaces, Essays in Mathematics and Its Applications in Honor of Vladimir Arnold, New York, Springer, 2016.  N.Y. Ozgur and N. Tas, Some fixed-circle theorems on metric spaces, Bull. Malays. Math. Sci. Soc., 42 (2019), pp. 1433-1449.  N.Y. Ozgur and N. Tas, Some fixed-circle theorems and discontinuity at fixed circle, AIP Conference Proceedings 1926, 020048 (2018).  N.Y. Ozgur, N. Tas, and U. Celik, New fixed-circle results on \$S\$-metric spaces, Bull. Math. Anal. Appl., 9 (2017), pp. 10-23.  N.Y. Ozgur and N. Tas, Fixed-circle problem on \$S\$-metric spaces with a geometric viewpoint, Facta Universitatis. Series: Mathematics and Informatics, 34 (3) (2019), pp. 459-472.  M. Ozturk, Common fixed point theorems satisfying contractive type conditions in complex-valued metric spaces, Abstr. Appl. Anal., 2014 (2014), 7 pp.  M. Ozturk and N. Kaplan, Common fixed points of \$f\$-contraction mappings in complex-valued metric spaces, Math. Sci., 8 (2014), 7 pp.  M. Ozturk and N. Kaplan, Some common coupled fixed points of mappings satisfying contractive conditions with rational expressions in complex-valued \$G_b\$-metric spaces, Bangmod Int. J. Math. & Comp. Sci., 1 (2015), pp. 190-204.  N. Priyobarta, Y. Rohen, and N. Mlaiki, Complex valued Sb-metric spaces, J. Math. Anal., 8 (2017), pp. 13-24.  M.M. Rezaee, S. Sedghi, and K. S. Kim, Coupled common fixed point results in ordered \$S\$-metric spaces, Nonlinear Funct. Anal. Appl., 23 (2018), pp. 595-612.  B.E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc., 226 (1977), pp. 257-290.  S. Sedghi, N. Shobe, and A. Aliouche, A generalization of fixed point theorems in \$S\$-metric spaces, Mat. Vesnik, 64 (2012), pp. 258-266.  R.J. Shahkoohi and Z. Bagheri, Rational Geraghty contractive mappings and fixed point theorems in ordered \$b_2\$-metric spaces, Sahand Commun. Math. Anal., 13 (1) (2019), pp. 179-212.  H. Shayanpour and A. Nematizadeh, Common fixed point theory in modified intuitionistic probabilistic metric spaces with common property \$(E.A.)\$, Sahand Commun. Math. Anal., 13 (1) (2019), pp. 31-50.  N. Tas, N.Y. Ozgur, and N. Mlaiki, New types of \$F_c\$-contractions and the fixed-circle problem, Mathematics, 6 (2018), 9 pp.  R.K. Verma and H.K. Pathak, Common fixed point theorems using property \$(E.A)\$ in complex-valued metric spaces, Thai J. Math., 11 (2013), pp. 347-355.
SCMA دانشگاه مراغه Sahand Communications in Mathematical Analysis 2322-5807 دانشگاه مراغه 37414 10.22130/scma.2019.69719.273 Research Paper On the Monotone Mappings in CAT(0) Spaces On the Monotone Mappings in CAT(0) Spaces Afkhami Taba Davood Department of Mathematics, Bandar Abbas Branch, Islamic Azad University, P.O.Box 79158-93144, Bandar Abbas, Iran. Dehghan Hossein Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Gava Zang, P.O.Box 45137-66731, Zanjan, Iran 01 06 2020 17 2 107 117 08 08 2017 01 09 2019 Copyright © 2020, دانشگاه مراغه. 2020 https://scma.maragheh.ac.ir/article_37414.html

In this paper, we first introduce a monotone mapping and its resolvent in general metric spaces.Then, we give two new iterative methods  by combining the resolvent method with Halpern's iterative method and viscosity approximation method for  finding a fixed point of monotone mappings and a solution of variational inequalities. We prove convergence theorems of the proposed iterations  in CAT(0) metric spaces.

Monotone mapping Nonexpansive mapping Variational inequality Fixed point CAT(0) metric space
 S. Alizadeha, H. Dehghan, and F. Moradlou, \$Delta\$-convergence theorems for inverse-strongly monotone mappings in CAT(0) spaces, Fixed Point Theory, 19(1) (2018), pp. 45-56.  M. Asadi, Fixed points and common fixed points of mappings on CAT(0) spaces, Fixed Point Theory, 14(1) (2013), pp. 29-38.  M. Asadi, Some notes on fixed point sets in CAT(0) spaces, Adv. Fixed Point Theory, 4(3) (2014), pp. 395-401.  M. Asadi, S.M. Vaezpour, and H. Soleimani, \$alpha\$-Nonexpansive Mappings on CAT(0) spaces, World Applied Sciences Journal, 11(10) (2010), pp. 1303-1306.  W. Ballmann, Lectures on Spaces of Nonpositive Curvature, in: DMV Seminar Band, vol. 25, Birkhauser, Basel, (1995)  I.D. Berg and I.G. Nikolaev, Quasilinearization and curvature of Alexandrov spaces, Geom. Dedicata 133 (2008), pp. 195-218.  M. Bridson and A. Haefliger, Metric Spaces of Nonpositive Curvature, Springer-Verlag, Berlin, Heidelberg, New York, (1999).  A. Cuntavepanit and B. Panyanak, Strong convergence of modified Halpern iterations in CAT(0) spaces. Fixed Point Theory Appl. 869458, (2011) doi:10.1155/2011/869458  H. Dehghan and J. Rooin, A characterization of metric projection in CAT(0) spaces, arXiv:1311.4174v1, 2013.  S. Dhompongsa, W.A. Kirk, and B. Sims, Fixed points of uniformly lipschitzian mappings, Nonlinear Anal., 65 (2006), pp. 762-772.  S. Dhompongsa, W.A. Kirk, and B. Panyanak, Nonexpansive set-valued mappings in metric and Banach spaces, J. Nonlinear and Convex Anal., 8 (2007), pp. 35-45.  S. Dhompongsa and B. Panyanak, On \$Delta\$-convergence theorems in CAT(0) spaces, Comput. Math. Appl., 56 (2008), pp. 2572-2579.  B.A. Kakavandi and M. Amini, Duality and subdifferential for convex functions on complete CAT(0) metric spaces, Nonlinear Anal., 73 (2010), pp. 3450-3455.  B.A. Kakavandi, Weak topologies in complete CAT(0) metric spaces, Proc. Amer. Math. Soc., 141 (2013), pp. 1029-1039.  J.K. Kim and T.M. Tuyen, New iterative methods for finding a common zero of a finite family of monotone operators in Hilbert spaces, Bull. Korean Math. Soc., 54 (2017), pp. 1347-1359.  W.A. Kirk and B. Panyanak, A concept of convergence in geodesic spaces, Nonlinear Anal., 68 (2008), pp. 3689-3696.  W.A. Kirk, Geodesic geometry and fixed point theory, in Seminar of Mathematical Analysis (Malaga/Seville, 2002/2003), vol. 64 of Colecc. Abierta, pp. 195-225, University of Seville, Secretary Publication, Seville, Spain, (2003).  T.C. Lim, Remarks on some fixed point theorems, Proc. Amer. Math. Soc., 60 (1976), pp. 179-182.  A. Papadopoulos, Metric Spaces, Convexity and Nonpositive Curvature, IRMA Lectures in Mathematics and Theoretical Physics, 6. European Mathematical Society (EMS), Zurich, 2005.  S. Ranjbar, Strong convergence of a composite Halpern type iteration for a family of nonexpansive mappings in CAT(0) spaces, An. Stiint. Univ. Ovidius Constanta Ser. Mat. 3 (2017).  H.K. Xu, Iterative algorithms for nonlinear operators, J. London Math. Soc., 66 (2002), pp. 240-256.
SCMA دانشگاه مراغه Sahand Communications in Mathematical Analysis 2322-5807 دانشگاه مراغه 38391 10.22130/scma.2019.95982.515 Research Paper Best Proximity Point Results for Almost Contraction and Application to Nonlinear Differential Equation Best Proximity Point Results for Almost Contraction and Application to Nonlinear Differential Equation Hussain Azhar Department of Mathematics, University of Sargodha, Sargodha-40100, Pakistan. Abbas Mujahid Department of Mathematics, Government College University, Lahore 54000, Pakistan and Department of Mathematics and Applied Mathematics, University of Pretoria Hatfield 002, Pretoria, South Africa. Adeel Muhammad Department of Mathematics, University of Sargodha, Sargodha-40100, Pakistan. Kanwal Tanzeela Department of Mathematics, University of Sargodha, Sargodha-40100, Pakistan. 01 06 2020 17 2 119 138 18 10 2018 22 01 2020 Copyright © 2020, دانشگاه مراغه. 2020 https://scma.maragheh.ac.ir/article_38391.html

Berinde [V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum {bf 9} (2004), 43-53] introduced almost contraction mappings and proved Banach contraction principle for such mappings. The aim of this paper is to introduce the notion of multivalued almost \$Theta\$- contraction mappings andto prove some best proximity point results for this new class of mappings. As applications, best proximity point and fixed point results for weak single valued \$Theta\$-contraction mappings are obtained. Moreover, we give an example to support the results presented herein. An application to a nonlinear differential equation is also provided.

Almost contraction \$Theta\$-contraction best proximity points differential equation
SCMA دانشگاه مراغه Sahand Communications in Mathematical Analysis 2322-5807 دانشگاه مراغه 37469 10.22130/scma.2018.94775.506 Research Paper Inequalities of Ando's Type for \$n\$-convex Functions Inequalities of Ando's Type for \$n\$-convex Functions Mikic Rozarija University of Zagreb, Faculty of Textile Technology, 10000 Zagreb, Croatia. Pečarić Josip RUDN University, Miklukho-Maklaya str. 6, 117198 Moscow, Russia. 01 06 2020 17 2 139 159 30 09 2018 30 11 2019 Copyright © 2020, دانشگاه مراغه. 2020 https://scma.maragheh.ac.ir/article_37469.html

By utilizing different scalar equalities obtained via Hermite's interpolating polynomial, we will obtain lower and upper bounds for the difference in Ando's inequality and in the Edmundson-Lah-Ribariv c inequality for solidarities that hold for a class of \$n\$-convex functions. As an application, main results are applied to some operator means and relative operator entropy.

Solidarities Ando's inequality Edmundson-Lah-Ribariv c inequality \$n\$-convex functions Operator means
 R.P. Agarwal and P.J.Y. Wong, Error inequalities in polynomial interpolation and their applications, Kluwer Academic Publishers, Dordrecht, Boston, London, 1993.  J.S. Aujla and H.L. Vasudeva, Inequalities involving Hadamard product and operator means, Math. Japon., 42 (1995), pp. 265-272.  M.D. Choi, A Schwarz inequality for positive linear maps on \$C^ast-\$algebras, Ill. J. Math., 18 (1974), pp. 565-574.  M.D. Choi, Inequalities related to Heron means for positive operators, J. Math. Inequal., 11 (2017), pp. 217-223.  C. Davis, A Schwarz inequality for convex operator functions, Proc. Amer. Math. Soc., 8 (1957), pp. 42-44.  J.I. Fujii, M. Fujii and Y. Seo, An extension of the Kubo-Ando theory: Solidarities, Math. Japonica, 35 (1990), pp. 387-396.  T. Furuta, J. Micic Hot, J. Pecaric and Y. Seo, Mond-Pecaric method in operator inequalities, Monographs in Inequalities 1, Element, Zagreb, 2005.  M. Fujii, J. Micic Hot, J. Pecaric and Y. Seo, Recent developments of Mond-Pecaric method in operator inequalities, Monographs in Inequalities 4, Element, Zagreb, 2012.  F. Kubo and T. Ando, Means of positive linear operators, Math. Ann., 246 (1980), pp. 205-224.  R. Mikic, D Pecaric, and J. Pecaric, Inequalities of the Edmundson-Lah-Ribariv c type for \$n\$-convex functions with applications, Ukr. Math. J., In Press.  R. Mikic, J. Pecaric, and I. Peric, Reverses of Ando and Davis-Choi inequalities, J. Math. Inequal., 9 (2015), pp. 615-630.  R. Mikic, J. Pecaric, I. Peric, and Y. Seo, The generalized Tsallis operator entropy via solidarity, J. Math. Inequal., 10 (2016), pp. 269-283.  I. Nikoufar and M. Alinejad, Bounds of generalized relative operator entropies, Math. Inequal. Appl., 20 (2017), pp. 1067-1078.  J.E. Pecaric, F. Proschan, and Y.L. Tong, Convex functions, Partial orderings and statistical applications, Academic Press Inc., San Diego 1992.  S. Sheybani, M. Erfanian, and H.R. Moradi, New inequalities for operator concave functions involving positive linear maps, Math. Inequal. Appl., 21 (2018), pp. 1167-1174.  M. Taati, S. Moradi, and S. Najafzadeh, Some properties and results for certain subclasses of starlike and convex functions, Sahand Commun. Math. Anal., 7 (2017), pp. 1-15.
SCMA دانشگاه مراغه Sahand Communications in Mathematical Analysis 2322-5807 دانشگاه مراغه 37836 10.22130/scma.2018.84950.427 Research Paper New Generalization of Darbo's Fixed Point Theorem via \$alpha\$-admissible Simulation Functions with Application New Generalization of Darbo's Fixed Point Theorem via \$alpha\$-admissible Simulation Functions with Application Monfared Hossein Department of Mathematics, Bilehsavar Branch, Islamic Azad University, Bilehsavar, Iran. Asadi Mehdi Department of Mathematics, Zanjan Branch, Islamic Azad University, Zanjan, Iran. Farajzadeh Ali Department of Mathematics, Razi University, Kermanshah, 67149, Iran. 01 06 2020 17 2 161 171 25 04 2018 17 12 2019 Copyright © 2020, دانشگاه مراغه. 2020 https://scma.maragheh.ac.ir/article_37836.html

In this paper, at first, we introduce \$alpha_{mu}\$-admissible, \$Z_mu\$-contraction and  \$N_{mu}\$-contraction via simulation functions. We prove some new fixed point theorems for defined class of contractions   via \$alpha\$-admissible simulation mappings, as well. Our results  can be viewed as extension of the corresponding results in this area.  Moreover, some examples and an application to functional integral equations are given to support the obtained results.

Measure of non-compactness Simulation functions \$alpha\$-admissible mappings Fixed point
 A. Aghajani, J. Banas, and N. Sabzali, Some generalizations of Darbo's fixed point theorem and applications, Bull. Belg. Math. Soc., Simon Stevin 20 (2013), pp. 345-358.  J. Bana's and K. Goebel, Measures of noncompactness in Banach spaces, in: Lecture Notes in Pure and Applied Mathematics, Dekker New York, 60, 1980.  J. Chen and X. Tang, Generalizations of Darbo's fixed point theorem via simulation functions with application to functional integral equations, J. Comput. Appl. Math., 296 (2016), pp. 564-575.  C.-M. Chen, E. Karapi nar, and D. O'regan, On \$(alpha-phi)\$-Meir-Keeler contractions on partial Hausdorff metric spaces, University Politehnica Of Bucharest Scientific, Bulletin-Series A-Applied Mathematics And Physics, 80 (2018), pp. 101-110.  G. Darbo, Punti unitti in transformazioni a condominio non compatto, Rend. Semin. Mat. Univ. Padova, 24 (1955), pp. 84-92.  A. Farajzadeha and A. Kaewcharoen, Best proximity point theorems for a new class of \$alpha-psi-\$ proximal contractive mappings, J. Non. Conv. Anal., 16 (2015), pp. 497-507.  A. Farajzadeha, P. Chuadchawna, and A. Kaewcharoen, Fixed point theorems for \$(alpha; eta; psi;xi)-\$contractive multi-valued mappings on \$ alpha-eta\$ complete partial metric spaces, J. Nonlinear Sci. Appl., 9 (2016), pp. 1977-1990.  M. Geraghty, On contractive mappings, Proc. Amer. Math. Soc., 40 (1973), pp. 604-608.  L. Gholizadeh and E. Karapi nar, Best proximity point results in dislocated metric spaces via \$R\$-functions, Revista da la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 112 (2018), pp. 1391-1407.  A. Hajji, A generalization of Darbo's fixed point and common solutions of equations in Banach spaces, Fixed Point Theory Appl. (2013), 2013:62.  E. Karapi nar and F. Khojasteh, An approach to best proximity points results via simulation functions, J. Fixed Point Theory Appl., 19 (2017), pp. 1983-–1995.  M. S. Khan, M. Swaleh, and S. Sessa, Fixed point theorems by altering distances between the points, Bull. Aust. Math. Soc., 30 (1984), pp. 1-9.  F. Khojasteh, S. Shukla, and S. Radenovic, A new approach to the study of fixed point theory for simulation function, Filomat, 29 (2015), pp. 1189-1194.  O. Popescu, Some new fixed point theorems for \$alpha\$-Geraghty contractive type maps in metric spaces, Fixed Point Theory Appl., (2014), 2014:190.  A.F. Roldan-Lopez-de-Hierro, E. Karapi nar, C. Roldan-Lopez-de-Hierro, and J. Martnez-Moreno, Coincidence point theorems on metric spaces via simulation functions, J. Comput. Appl. Math., 275 (2015), pp. 345-355.  A. Samadi and M.B. Ghaemi, An extension of Darbos theorem and its application, Abstr. Appl. Anal., 2014 (2014), Article ID 852324, 11 pages.  B. Samet, C. Vetro, and P. Vetro, Fixed point theorem for \$alpha-psi\$-contractive type mappings, Nonlinear Anal., 75 (2012), pp. 2154-2165.  P. Zangenehmehr, A.P. Farajzadeh, and S.M. Vaezpour, On fixed point theorems for monotone increasing vector valued mappings via scalarizing, Positivity, 19 (2015), pp. 333-340.
SCMA دانشگاه مراغه Sahand Communications in Mathematical Analysis 2322-5807 دانشگاه مراغه 39051 10.22130/scma.2019.107061.601 Research Paper Bornological Completion of Locally Convex Cones Bornological Completion of Locally Convex Cones Ayaseh Davood Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran. Ranjbari Asghar Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran. 01 06 2020 17 2 173 183 29 04 2019 22 01 2020 Copyright © 2020, دانشگاه مراغه. 2020 https://scma.maragheh.ac.ir/article_39051.html

In this paper, firstly, we obtain some new results about bornological convergence in locally convex cones (which was studied in ) and then we introduce the concept of bornological completion for locally convex cones. Also, we prove that the completion of a bornological locally convex cone is bornological. We illustrate the main result by an example.

Locally convex cones Bornological convergence Bornological cones Bornological completion
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SCMA دانشگاه مراغه Sahand Communications in Mathematical Analysis 2322-5807 دانشگاه مراغه 37409 10.22130/scma.2018.97329.523 Research Paper Generalized Continuous Frames for Operators Generalized Continuous Frames for Operators .Shekhar Chander Department of Mathematics Indraprastha college for Women, University of Delhi, Delhi 110054, India. Bhati Sunayana Department of Mathematics and Statistics, University college of Science, M.L.S. University, Udaipur, Rajasthan, India. Rathore G.S. Department of Mathematics and Statistics, University college of Science, M.L.S. University, Udaipur, Rajasthan, India. 01 06 2020 17 2 185 201 09 11 2018 02 12 2019 Copyright © 2020, دانشگاه مراغه. 2020 https://scma.maragheh.ac.ir/article_37409.html

In this note, the notion of generalized continuous K- frame in a Hilbert space is defined. Examples have been given to exhibit the existence of generalized continuous \$K\$-frames. A necessary and sufficient condition for the existence of a generalized continuous \$K\$-frame in terms of its frame operator is obtained and a characterization of a generalized continuous \$K\$-frame for \$ mathcal{H} \$ with respect to \$ mu \$ is given. Also, a sufficient condition for a generalized continuous \$K\$-frame is given.  Further, among other results, we prove that generalized continuous \$K\$-frames are invariant under a linear  homeomorphism. Finally, keeping in mind the importance of perturbation theory in various branches of applied mathematics, we study perturbation of \$K\$-frames and obtain conditions for the stability of generalized continuous \$K\$-frames.

Frames \$K\$-frames Continuous frames
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