2018
10
1
0
156
On generalized topological molecular lattices
2
2
In this paper, we introduce the concept of the generalized topological molecular lattices as a generalization of Wang's topological molecular lattices, topological spaces, fuzzy topological spaces, Lfuzzy topological spaces and soft topological spaces. Topological molecular lattices were defined by closed elements, but in this new structure we present the concept of the open elements and define a closed element by the pseudocomplement of an open element. We have two structures on a completely distributive complete lattice, topology and generalized cotopology which are not dual to each other. We study the basic concepts, in particular separation axioms and some relations among them.
1

1
15


Narges
Nazari
Department of Mathematics, University of Hormozgan, Bandarabbas, Iran.
Department of Mathematics, University of
Iran
nazarinargesmath@yahoo.com


Ghasem
Mirhosseinkhani
Department of Mathematics, Sirjan University of Technology, Sirjan, Iran.
Department of Mathematics, Sirjan University
Iran
gh.mirhosseini@yahoo.com
Topological molecular lattice
Generalized Topological molecular lattice
Generalized order homomorphism
Separation axiom
[[1] A.R. Aliabadi and A. Sheykhmiri, LGtopology, Bull. Iranian Math. Soc., 41 (2015), pp. 239258.##[2] T.S. Blyth, Lattice and Ordered Algebraic Structures, SpringerVerlag, London, 2005.##[3] G. Bruns, Darstellungen und Erweiterungen geordneter Mengen II, J. Reine Angew. Math., 210 (1962), pp. 123.##[4] K. ElSaady and F. AlNabbat, Generalized topological molecular lattices, Advances in Pure Mathematics, 5 (2015), pp. 552559.##[5] P.T. Johnstone, Stone spaces, Cambridge studies in Advanced Mathematics, Cambridge University press, cambridge, 1982.##[6] Y.M. Li, Exponentiable objects in the category of topological molecular lattices, Fuzzy sets and systems, 104 (1999), pp. 407414.##[7] J. Picado and A. Pultr, Frames and locales, Topology Without Points, Frontiers in Mathematics, BirkhauserSpringer AG, Basel, 2012.##[8] S. Roman, Lattice and ordered sets, Springer, New York, 2008.##[9] W.J. Thron, Latticeequivalence of topological spaces, Duke Math. J., 29 (1962), pp. 671679.##[10] G.J. Wang, Theory of topological molecular lattices, Fuzzy Sets and Systems, 47 (1992), pp. 351376.##[12] G.J. Wang, Generalized topological molecular lattices, Scientia Sinica, 8 (1984), pp. 785798.##]
Similar generalized frames
2
2
Generalized frames are an extension of frames in Hilbert spaces and Hilbert $C^*$modules. In this paper, the concept ''Similar" for modular $g$frames is introduced and all of operator duals (ordinary duals) of similar $g$frames with respect to each other are characterized. Also, an operator dual of a given $g$frame is studied where $g$frame is constructed by a primary $g$frame and an orthogonal projection. Moreover, a $g$frame is obtained by two the $g$frames and its operator duals are investigated. Finally, the dilation of $g$frames is studied.
1

17
28


Azadeh
Alijani
Department of Mathematics, Faculty of Science,
ValieAsr University of Rafsanjan, P.O. Box 7719758457, Rafsanjan, Iran.
Department of Mathematics, Faculty of Science,
Val
Iran
a.alijani57@gmail.com
Dual frame
Similar $g$frames
Frame operator
$g$frame
Operator dual frame
[[1] A. Alijani, Generalized frames with C*valued bounds and their operator duals, Filomat, 29 (2015), pp. 14691479.##[2] A. Alijani and M.A. Dehghan, $G$frames and their duals for Hilbert C*modules, Bull. Iranian Math. Soc., 38 (2012), pp. 567580.##[3] P.G. Casazza, The art of frame theory, Taiw. J. Math., 4 (2000), pp. 129201.##[4] P.G. Casazza and G. Kutyniok, Finite Frames: Theory and Applications, Brikhauser Basel, 2013.##[5] M.A. Dehghan and M.A. Hasankhani Fard, GDual frames in Hilbert spaces, U.P.B. Sci. Bull., Series A, 75 (2013), pp. 129140.##[6] M. Frank and D.R. Larson, Frames in Hilbert C*modules and C*algebra, J. Operator theory, 48 (2002), pp. 273314.##[7] D. Han, W. Jing, D. Larson, and R. Mohapatra, Riesz bases and their dual modular frames in Hilbert C*modules, J. Math. Anal. Appl., 343 (2008), pp. 246256.##[8] A. Khosravi and B. Khosravi, Fusion frames and $g$frames in Hilbert C*modules, Int. J. Wavelets Multiresolut. Inf. Process., 6 (2008), pp. 433446.##[9] A. Khosravi and B. Khosravi, gframes and modular Riesz bases in Hilbert C*modules, Int. J. Wavelets Multiresolut. Inf. Process., 10 (2012), pp. 112.##[10] E.C. Lance, Hilbert C*modules, A Toolkit for Operator Algebraists, University of Leeds, Cambridge University Press, 1995.##[11] A. Najati and A. Rahimi, Generalized frames in Hilbert spaces, Bull. Iran Math. Soc., 35 (2009), pp. 97109.##[12] W. Sun, GFrames and $g$Riesz bases, J. Math. Anal. Appl., 322 (2006), pp. 437452.##]
On $L^*$proximate order of meromorphic function
2
2
In this paper we introduce the notion of $L^{* }$proximate order of meromorphic function and prove its existence.
1

29
35


Sanjib
Datta
Department of Mathematics, University of Kalyani, P.O.Kalyani, DistNadia, PIN741235, West Bengal, India.
Department of Mathematics, University of
Iran
sanjib_kr_datta@yahoo.co.in


Tanmay
Biswas
Rajbari, Rabindrapalli, R. N. Tagore Road, P.O.Krishnagar, DistNadia, PIN741101, West Bengal, India.
Rajbari, Rabindrapalli, R. N. Tagore Road,
Iran
tanmaybiswas_math@rediffmail.com
Meromorphic function
$L^*$order
$L^*$ proximate order
[[1] I. Lahiri, Generalised proximate order of meromorphic functions, Mat. Vesnik, 41 (1989), pp. 916.##[2] S.M. Shah, On proximate orders of integral functions, Bull. Amer. Math. Soc., 52 (1984), pp. 326328.##[3] S.K. Singh and G.P. Barker, Slowly changing functions and their applications, Indian J. Math., 19 (1977), pp. 16.##[4] D. Somasundaram and R. Thamizharasi, A note on the entire functions of Lbounded index and Ltype, Indian J. Pure Appl. Math., 19 (1988), pp. 284293.##[5] G. Valiron, Lectures on the general theory of integral functions, Chelsea Publishing Company, 1949.##]
The spectral properties of differential operators with matrix coefficients on elliptic systems with boundary conditions
2
2
Let $$(Lv)(t)=sum^{n} _{i,j=1} (1)^{j} d_{j} left( s^{2alpha}(t) b_{ij}(t) mu(t) d_{i}v(t)right),$$ be a nonselfadjoint differential operator on the Hilbert space $L_{2}(Omega)$ with Dirichlettype boundary conditions. In continuing of papers [1012], let the conditions made on the operator $ L$ be sufficiently more general than [11] and [12] as defined in Section $1$. In this paper, we estimate the resolvent of the operator $L$ on the onedimensional space $ L_{2}(Omega)$ using some analytic methods.
1

37
46


Leila
Nasiri
Department of Mathematics and computer science, Faculty of science, Lorestan University, Khorramabad, Iran.
Department of Mathematics and computer science,
Iran
leilanasiri468@gmail.com


Ali
Sameripour
Department of Mathematics and computer science, Faculty of science, Lorestan University, Khorramabad, Iran.
Department of Mathematics and computer science,
Iran
asameripour@yahoo.com
Resolvent
Distribution of eigenvalues
Nonselfadjoint differential operators
[[1] K.Kh. Boimatov, Asymptotics of the spectrum of nonselfadjoint systems of secondorder differential operators, (Russian) Mat. Zametki, 51 (1992), pp. 816.##[2] K.Kh. Boimatov, Asymptotic behavior of the spectra of secondorder nonselfadjoint systems of differential operators, Mat. Zametki., 51 (1992), pp. 816.##[3] K.Kh. Boimatov, On the distribution of the eigenvalues of differential operators which depend polynominally on a small parameter, Bull. Iranian Math. Soc., 19 (1993), pp. 1326.##[4] K.Kh. Boimatov, The generalized Dirichlet problem associated with noncoercive bilinear forms, (Russian) Dokl. Akad. Nauk., 330, (1993), pp. 285290.##[5] K.Kh. Boimatov and A.G. Kostyuchenko, Distribution of eigenvalues of secondorder nonselfadjoint differential operators, (Russian) Vest. Moskov. Univ. Ser. I Mat. Mekh., 3 (1990), pp. 2431.##[6] K.Kh. Boimatov and A.G. Kostyuchenko, The spectral asymptotics of nonselfadjoint elliptic systems of differential operators in bounded domains, (Russian) Mat. Sb., 181 (1990), pp. 16781693.##[7] M.G. Gadoev, Spectral asymptotics of non selfadjoint degenerate elliptic operators with singular matrix coefficients on an integral, Ufa mathematical journal, 3 (2011), pp. 2653. ##[8] I.C. Gokhberg and M.G. Krein, Introduction to the Theory of linear nonselfadjoint operators in Hilbert space, Amer. Math. Soc., Providence, R. I., 1969.##[9] T. Kato, Perturbation Theory for Linear operators, Springer, New York, 1966.##[10] L. Nasiri and A. Sameripour, Notes on spectral featurs of degenerate nonselfadjoint differential operators on elliptic systems and ldimensional Hilbert spaces, Math. Sci. Lett., 6 (2017). ##[11] A. Sameripour and K. Seddigh, Distribution of eigenvalues of nonselfadjoint elliptic systems on the domain boundary, (Russian) Mat. Zametki, 61 (1997), pp. 463467.##[12] A. Sameripour and K. Seddighi, On the spectral properties of generelized nonselfadjoint elliptic systems of differential operators degenerated on the boundary of domain, Bull. Iranian Math. Soc., 24 (1998), pp. 1532.##[13] A.A. Shkalikov, Tauberian type theorems on the distribution of zeros of holomorphic functions, Mat. Sb., 123 (1984), pp. 317347.##]
Existence of three solutions for a class of quasilinear elliptic systems involving the $p(x)$Laplace operator
2
2
The aim of this paper is to obtain three weak solutions for the Dirichlet quasilinear elliptic systems on a bonded domain. Our technical approach is based on the general three critical points theorem obtained by Ricceri.
1

47
60


Ali
Taghavi
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.
Department of Mathematics, Faculty of Mathematical
Iran
taghavi@umz.ac.ir


Ghasem
Alizadeh Afrouzi
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.
Department of Mathematics, Faculty of Mathematical
Iran
afrouzi@umz.ac.ir


Horieh
Ghorbani
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.
Department of Mathematics, Faculty of Mathematical
Iran
h.ghorbani@stu.umz.ac.ir
Variable exponent Sobolev space
p(x)Laplacian
Three solutions
Dirichlet problem
[[1] E. Acerbi and G. Mingione, Regularity results for stationary electrorheological fluids, Arch. Ration. Mech. Anal., 156 (2001), pp. 121140.##[2] X.L. Fan, J. Shen, and D. Zhao, Sobolev embedding theorems for spaces Wk,p(x)(Ω), J. Math. Anal. Appl., 262 (2001), pp. 749760.##[3] X.L. Fan and D. Zhao, On the spaces Lp(x)(Ω) and W1,p(x)(Ω), J. Math. Anal. Appl., 263 (2001), pp. 424446.##[4] X.L. Fan and Q.H. Zhang, Existence of solutions for p(x)Laplacian Dirichlet problems, Nonlinear Anal., 52 (2003), pp. 18431852.##[5] A.El. Hamidi, Existence result to elliptic systems with nonstandard growth conditions, J. Math. Anal. Appl., 300 (2004), pp. 3042.##[6] J.J. Liu and X.Y. Shi, Existence of three solutions for a class of quasilinear elliptic systems involving the (p(x), q(x))Laplacian, Nonlinear Anal., 71 (2009), pp. 550557.##[7] M. Mihailescue, Existence and multiplicity of solutions for a Neumann problem involving the p(x)Laplace operator, Nonlinear Anal., 2007 (67), pp. 14191425.##[8] B. Ricceri, A three critical points theorem revisited, Nonlinear Anal., 70 (2009), pp. 30843089.##[9] B. Ricceri, A general variational principle and some of its applications, J. Comput. Appl. Math., 113 (2000), pp. 401410.##[10] B. Ricceri, Existence of three solutions for a class of elliptic eigenvalue problem, Math. Comput. Modelling., 32 (2000), pp. 14851494.##[11] M. Ruzicka, Electrorheological Fluids: Modeling and Mathematical Theory, Lecture Notes in Math, vol. 1784, SpringerVerlag, Berlin, 2000.##[12] H.H. Yin, Existence of three solutions for a Neumann problem involving the p(x)Laplace operator, Math. Meth. Appl. Sci., 35 (2012), pp. 307313.##[13] V.V. Zhikov, Averaging of functionals of the calculus of variations and elasticity theory, Math. USSR Izv. 29 (1987), pp. 3336.##]
Products Of EP Operators On Hilbert C*Modules
2
2
In this paper, the special attention is given to the product of two modular operators, and when at least one of them is EP, some interesting results is made, so the equivalent conditions are presented that imply the product of operators is EP. Also, some conditions are provided, for which the reverse order law is hold. Furthermore, it is proved that $P(RPQ)$ is idempotent, if $RPQ$† has closed range, for orthogonal projections $P,Q$ and $R$.
1

61
71


Javad
FarokhiOstad
Department of Mathematics, Faculty of Mathematics and Statistics, University of Birjand, Birjand, Iran.
Department of Mathematics, Faculty of Mathematics
Iran
javadfarrokhi90@gmail.com


Ali Reza
Janfada
Department of Mathematics, Faculty of Mathematics and Statistics, University of Birjand, Birjand, Iran.
Department of Mathematics, Faculty of Mathematics
Iran
ajanfada@birjand.ac.ir
Closed range
EP operators
MoorePenrose inverse
Hilbert $C^*$module
[[1] S. Campbell and C.D. Meyer, Continuity properties of the Drazin pseudo inverse, Linear Algebra and Its Applications, 10 (1975), pp. 7783.##[2] S. Campbell and C.D. Meyer, EP operators and generalized inverses, Canadian Math. Bull., 18 (1975), pp. 327333.##[3] C.Y. Deng and H.K. Du, Representations of the MoorePenrose inverse for a class of 2 by 2 block operator valued partial matrices, Linear and Multilinear Algebra, 58 (2010), pp. 1526.##[4] D.S. Djordjevic, Further results on the reverse order law for generalized inverses, SIAM J. Matrix Anal. Appl., 29 (2007), pp. 12421246.##[5] D.S. Djordjevic and N.C. Dincic, Reverse order law for the MoorePenrose inverse, J. Math. Anal. Appl., 361 (2010), pp. 252261.##[6] J. Farokhiostad and M. Mohammadzadeh Karizaki, The reverse order law for EP modular operators, J. Math. Computer Sci. 16 (2016), pp. 412418.##[7] M. Frank, Geometrical aspects of Hilbert C*modules, Positivity, 1999, pp. 215243.##[8] M. Frank, Selfduality and C*reflexivity of Hilbert C*modules, Z. Anal. Anwendungen, 1990, pp. 165176.##[9] S. Izumino, The product of operators with closed range and an extension of the revers order law, Tohoku Math. J.,34 (2) (1982), pp. 4352.##[10] E.C. Lance, Hilbert C*Modules, LMS Lecture Note Series 210, Cambridge Univ. Press, 1995.##[11] M. Mohammadzadeh Karizaki and D.S. Djordjevic, Commuting C* modular operators, Aequationes Mathematicae 6 (2016), pp. 11031114. ##[12] M. Mohammadzadeh Karizaki, M. Hassani, and M. Amyari, MoorePenrose inverse of product operators in Hilbert C*modules, Filomat, 8 (2016), pp. 33973402.##[13] M. Mohammadzadeh Karizaki, M. Hassani, M. Amyari, and M. Khosravi, Operator matrix of MoorePenrose inverse operators on Hilbert C*modules, Colloq. Math., 140 (2015), pp. 171182.##[14] M.S. Moslehian, K. Sharifi, M. Forough, and M. Chakoshi, MoorePenrose inverse of Gram operator on Hilbert C*modules, Studia Math., 210 (2012), pp. 189196.##[15] G.J. Murphy, C*algebras and operator theory, Academic Press Inc., Boston, MA, 1990.##[16] K. Sharifi, The product of operators with closed range in Hilbert C*modules, Linear Algebra Appl., 435 (2011), pp. 11221130.##[17] K. Sharifi, EP modular operators and their products, J. Math. Anal. Appl., 419 (2014), pp. 870877. ##[18] K. Sharifi and B. Ahmadi Bonakdar, The reverse order law for MoorePenrose inverses of operators on Hilbert C* modules, Bull. Iran. Math. Soc., 42 (2016), pp. 53 60.##[19] Q. Xu and L. Sheng, Positive semidefinite matrices of adjointable operators on Hilbert C*modules, Linear Algebra Appl. 428 (2008), pp. 9921000.##]
$C^{*}$semiinner product spaces
2
2
In this paper, we introduce a generalization of Hilbert $C^*$modules which are preFinsler modules, namely, $C^{*}$semiinner product spaces. Some properties and results of such spaces are investigated, specially the orthogonality in these spaces will be considered. We then study bounded linear operators on $C^{*}$semiinner product spaces.
1

73
83


Saeedeh
Shamsi Gamchi
Department of Mathematics, Payame Noor University, P.O. Box 193953697 ,Tehran, Iran.
Department of Mathematics, Payame Noor University,
Iran
saeedeh.shamsi@gmail.com


Mohammad
Janfada
Department of Mathematics, Ferdowsi University of Mashhad, P.O.Box 115991775, Mashhad Iran.
Department of Mathematics, Ferdowsi University
Iran
mjanfada@gmail.com


Asadollah
Niknam
Department of Mathematics, Ferdowsi University of Mashhad, P.O.Box 115991775, Mashhad Iran.
Department of Mathematics, Ferdowsi University
Iran
dassamankin@yahoo.co.uk
Semiinner product space
Hilbert $C^*$module
$C^*$algebra
[[1] M. Amyari and A. Niknam, A note on Finsler modules, Bulletin of the Iranian Mathematical Society, 29 (2003), pp. 7781.## ##[2] D. Bakic and B. Guljas, On a class of module maps of Hilbert C*modules, Mathematica communications, 7 2 (2002), pp. 177192.## ##[3] G. Birkhoff, Orthogonality in linear metric spaces, Duke Math. J., 1 (1935), pp. 169172.## ##[4] S.S. Dragomir, SemiInner Products and Applications, Nova Science Publishers, Hauppauge, New York, 2004.## ##[5] S.S. Dragomir, J.J. Koliha, and Melbourne, Two mappings related to semiinner products and their applications in geometry of normed linear spaces, Applications of Mathematics, 45 (2000), pp. 337355.## ##[6] S.G. ElSayyad and S.M. Khaleelulla , *semiinner product algebras of type(p), Zb. Rad. Prirod. Mat. Fak. Ser. Mat., 23 (1993), pp. 175187.## ##[7] G.D. Faulkner, Representation of linear functionals in a Banach space, Rocky Mountain J. Math., 7 (1977), pp. 789792.## ##[8] J.R. Giles, Classes of semiinnerproduct spaces, Trans. Amer. Math. Soc., 129 (1967), pp. 436446.## ##[9] R.C. James, Orthogonality and linear functionals in normed linear spaces, Trans. Amer. Math. Soc., 61 (1947), pp. 265292.## ##[10] B.E. Johnson, Centralisers and operators reduced by maximal ideals, J. London Math. Soc., 43 (1986), pp. 231233.## ##[11] I. Kaplansky, Modules over operator algebras, Amer. J. Math., (75) (1953), pp. 839858.## ##[12] D.O. Koehler, A note on some operator theory in certain semiinnerproduct spaces, Proc. Amer. Math. Soc., 30 (1971), pp. 363366.## ##[13] G. Lumer, Semiinnerproduct spaces, Trans. Amer. Math. Soc., 100 (1961), pp. 2943.## ##[14] G. Lumer, On the isometries of reflexive Orlicz spaces, Ann. Inst. Fourier (Grenoble)., 13 (1963), pp. 99109.## ##[15] E.C. Lance, Hilbert C*modules . a toolkit for operator algebraists, London Math. Soc. Lecture Note Series, Cambridge Univ. Press, Cambridge, 1995.## ##[16] B. Nath, On generalization of semiinner product spaces, Math. J. Okayama Univ., 15 (1971), pp. 16.## ##[17] E. Pap and R. Pavlovic, Adjoint theorem on semiinner product spaces of type (p), Zb. Rad. Prirod. Mat. Fak. Ser. Mat., 25 (1995), pp. 3946.## ##[18] W.L. Paschke, Inner product modules over B*algebras, Trans. Amer. Math. Soc., 182 (1973), pp. 443468.## ##[19] N.C. Phillips and N. Weaver, Modules with norms which take values in a C*algebra, Pacific J. of Maths., 185 (1998), pp. 163181.##[20] C. Puttamadaiah and H. Gowda, On generalised adjoint abelian operators on Banach spaces, Indian J. Pure Appl. Math., 17 (1986), pp. 919924.## ##[21] M.A. Rieffel, Induced representations of C*algebras, Adv. Math., 13 (1974), pp. 176257.## ##[22] B. Rzepecki, On fixed point theorems of Maia type, Publications de l'Institut Mathématique, 28 (1980), pp. 179186.## ##[23] E. Torrance, Strictly convex spaces via semiinnerproduct space orthogonality, Proc. Amer. Math. Soc., 26 (1970), pp. 108110.## ##[24] H. Zhang and J. Zhang, Generalized semiinner products with applications to regularized learning, J. Math. Anal. Appl., 372 (2010), pp. 181196.##]
Some fixed point theorems for $C$class functions in $b$metric spaces
2
2
In this paper, via $C$class functions, as a new class of functions, a fixed theorem in complete $b$metric spaces is presented. Moreover, we study some results, which are direct consequences of the main results. In addition, as an application, the existence of a solution of an integral equation is given.
1

85
96


Arslan
Hojat Ansari
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
Department of Mathematics, Karaj Branch,
Iran
analsisamirmath2@gmail.com


Abdolrahman
Razani
Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran.
Department of Pure Mathematics, Faculty of
Iran
razani@ipm.ir
Fixed point
Complete metric space
$b$metric space
$C$class function
[[1] A. Aghajani, M. Abbas, and J.R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered bmetric spaces, Math. Slovaca, 4 (2014), pp. 941960.##[2] A.H. Ansari, Note on φψcontractive type mappings and related fixed point, The 2nd regional conference on mathematics and applications, PNU, 2014, pp. 377380.##[3] A.H. Ansari, S. Chandok, and C. Ionescu, Fixed point theorems on bmetric spaces for weak contractions with auxiliary functions, J. Inequal. Appl., 429 (2014), pp. 117.##[4] H. Aydi, M. Bota, E. Karapinar, and S. Mitrovic, A fixed point theorem for setvalued quasicontractions in bmetric spaces, Fixed Point Theory Appl., 88 (2012).##[5] I.A. Bakhtin, The contraction mapping principle in quasimetric spaces (Russian), Func. An., Gos. Ped. Inst. Unianowsk, 30 (1989), pp. 2637.##[6] M. Boriceanu, Strict fixed point theorems for multivalued operators in bmetric spaces, Int. J. Modern Math., 4 (2009), pp. 285301.##[7] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations int egrales, Fund. Math., 3 (1922), pp. 133181.##[8] S. Czerwik, Contraction mappings in bmetric spaces, Acta Math. Inf. Univ. Ostrav., 1 (1993), pp. 511.##[9] S. Czerwik, Nonlinear setvalued contraction mappings in bmetric spaces, Atti Sem. Mat. Fis. Univ. Modena, 46 (1998), pp. 263276.##[10] Z.M. Fadail, A.G.B. Ahmad, A.H. Ansari, S. Radenovic, and M. Rajovic, Some common fixed point results of mappings in 0σcomplete metriclike spaces via new function, Appl. Math. Sci., 9 (2015), pp. 41094127.##[11] R.H. Haghi, Sh. Rezapour, and N. Shahzad, Some fixed point generalizations are not real generalizations, Nonlinear Anal., 74 (2011), pp. 17991803.##[12] N. Hussain, V. Parvaneh, J.R. Roshan, and Z. Kadelburg, Fixed points of cyclic weakly (ψ, φ, L, A, B)contractive mappings in ordered bmetric spaces with applications, Fixed Point Theory Appl., 256 (2013), pp. 118.##[13] M.S. Khan, M. Swaleh, and S. Sessa, Fixed point theorems by altering distances between the points, Bull. Austral. Math. Soc., 30 (1984), pp. 19.##]
Convergence of Integro Quartic and Sextic BSpline interpolation
2
2
In this paper, quadratic and sextic Bsplines are used to construct an approximating function based on the integral values instead of the function values at the knots. This process due to the type of used Bsplines (fourth order or sixth order), called integro quadratic or sextic spline interpolation. After introducing the integro quartic and sextic Bspline interpolation, their convergence is discussed. The interpolation errors are studied. Numerical results illustrate the efficiency and effectiveness of the new interpolation method.
1

97
108


Jafar
Ahmadi Shali
Department of Statistics, Faculty of Mathematical Science, University of Tabriz, Tabriz, Iran.
Department of Statistics, Faculty of Mathematical
Iran
j_ahmadishali@tabrizu.ac.ir


Ahmadreza
Haghighi
Department of Mathematics, Faculty of Science, Technical and Vocational University(TVU), Tehran, Iran and Department of Mathematics, Faculty of Science, Urmia University of technology, P.O.Box 5716617165, UrmiaIran.
Department of Mathematics, Faculty of Science,
Iran
ah.haghighi@gamil.com


Nasim
Asghary
Department of Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, Iran.
Department of Mathematics, Islamic Azad University
Iran
nasim.asghary@gmail.com


Elham
Soleymani
Department of Mathematics, Faculty of Science, Urmia University of technology, P.O.Box 5716617165, Urmia, Iran.
Department of Mathematics, Faculty of Science,
Iran
elham13829@gamil.com
Integro interpolation quartic Bspline
Integro interpolation sextic Bspline
Convergence
[[1] C.de Boor, A Practical Guide to Spline Interpolation, SpringerVerlag, New York, 1978.##[2] A.R. Haghighi and M. Roohi, The fractional cubic spline interpolation without using the derivative values, Indian Journal of Science and Technology, 5 (2012), pp. 34333439.##[3] H. Behforooz, Approximation by integro cubic splines, Appl. Math. Comput., 175 (2006), pp. 815.##[4] H. Behforooz, Interpolation by integro quintic splines Appl. Math. Comput., 216 (2010), pp. 364367.##[5] F.G. Lang, X.P, On integro quartic spline interpolation, Appl. Math. Comput., 236 (2012), pp. 42144226.##[6] T. Wu and X.Zhang, Integro sextic spline interpolation and its super convergence, Appl. Math. Comput., 219 (2013), pp. 64316436.##[7] R.H. Wang, Numerical Approximation, Higher Education Press, Higher Education Press, Beijing, 1999.##[8] L. Schumaker, Spline Functions: Basic Theory, Cambridge University Press, Cambridge, 2007.##]
Somewhat pairwise fuzzy $alpha$irresolute continuous mappings
2
2
The concept of somewhat pairwise fuzzy $alpha$irresolute continuous mappings and somewhat pairwise fuzzy irresolute $alpha$open mappings have been introduced and studied. Besides, some interesting properties of those mappings are given.
1

109
118


Ayyarasu
Swaminathan
Department of Mathematics (FEAT),Annamalai University, Annamalainagar, Tamil Nadu608 002, India.
Department of Mathematics (FEAT),Annamalai
Iran
asnathanway@gmail.com
Somewhat pairwise fuzzy $alpha$irresolute continuous mapping
Somewhat pairwise fuzzy irresolute $alpha$open mapping
[[1] K.K. Azad, On fuzzy semicontinuity, fuzzy almost continuity and fuzzy weakly continuity, J. Math. Anal. Appl., 82 (1981), pp. 1432.##[2] C.L. Chang, Fuzzy topological spaces, J.Math.Anal.Appl.,24 (1968), pp. 182190.##[3] K.R. Gentry and Hughes B. Hoyle, III, Somewhat continuous functions, Czech. Math. Journal 21 (1971), pp. 512.##[4] Y.B. Im, J.S. Lee, and Y.D. Cho, Somewhat fuzzy αirresolute continuous mappings, Far East J. Math. Sci.70 (2012), pp. 145155.##[5] A. Kandil and M.E. ElShafee, Biproximities and fuzzy bitopological spaces, Simon Steviv, 63 (1989), pp. 4566.##[6] R. Prasad, S. Thakur, and R.K. Sand, Fuzzy αirresolute mappings, J. Fuzzy Math. 2 (1994), pp. 335339.##[7] M.K. Singal and N. Rajvanshi, Fuzzy αsets and alphacontinuous maps, Fuzzy Sets and Systems, 48 (1992), pp. 383390.##[8] G. Thangaraj and G. Balasubramanian, On somewhat fuzzy αcontinuous functions, J. Fuzzy Math. 16 (2008), pp. 641651.##[9] L.A. Zadeh, Fuzzy sets, Inform. And Control, 8 (1965), pp. 338353.##]
$L$Topological Spaces
2
2
By substituting the usual notion of open sets in a topological space $X$ with a suitable collection of maps from $X$ to a frame $L$, we introduce the notion of Ltopological spaces. Then, we proceed to study the classical notions and properties of usual topological spaces to the newly defined mathematical notion. Our emphasis would be concentrated on the well understood classical connectedness, quotient and compactness notions, where we prove the Thychonoff's theorem and connectedness property for ultra product of $L$compact and $L$connected topological spaces, respectively.
1

119
133


Ali
Bajravani
Department of Mathematics, Faculty of Basic Sciences, Azarbaijan Shahid Madani University, Tabriz, I. R. Iran.
Department of Mathematics, Faculty of Basic
Iran
bajravani1305@gmail.com
Compact Spaces
Connected Spaces
Frame
[[1] A. Bajravani and A. Rastegar, On the Smoothness of Functors, Iranian Journal of Mathematical Sciences and Informatics., 5(2010), pp. 2739.##[2] E. Bredon Glen, Topology and Geometry, Graduate Texts in Mathematics 139, Springer, 1993.##[3] S. Burris and H.P. Sankappanavar, A Course in Universal Algebra, SpringerVerlag, 1981.##[4] A. Hatcher, Algebraic Topology, Cambridge University Press; 2002.##[5] J.R. Munkres, Topology, Second Edition, Prentice Hall, Inc; 2000.##[6] D.G. Wright, Thychonoff's Theorem, Proceedings of the A. M. S., 120, 1994.##]
Fuzzy $e$regular spaces and strongly $e$irresolute mappings
2
2
The aim of this paper is to introduce fuzzy ($e$, almost) $e^{*}$regular spaces in $check{S}$ostak's fuzzy topological spaces. Using the $r$fuzzy $e$closed sets, we define $r$($r$$theta$, $r$$etheta$) $e$cluster points and their properties. Moreover, we investigate the relations among $r$($r$$theta$, $r$$etheta$) $e$cluster points, $r$fuzzy ($e$, almost) $e^{*}$regular spaces and their functions.
1

135
156


Veerappan
Chandrasekar
Department of Mathematics, Kandaswami Kandar's College, Pvelur638 182, Tamil Nadu, India.
Department of Mathematics, Kandaswami Kandar'
Iran
vckkc3895@gmail.com


Somasundaram
Parimala
Research Scholar (Part Time), Department of Mathematics, Kandaswami Kandar's College, Pvelur638 182, Tamil Nadu, India.
Research Scholar (Part Time), Department
Iran
pspmaths@gmail.com
Fuzzy topology
$r$fuzzy $e$open (closed) sets
$r$($r$$theta$
$r$$etheta$) $e$cluster points
$r$fuzzy ($e$
almost) $e^{*}$regular spaces
(strongly
$theta$) $e$irresolute mappings
[[1] C.L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), pp. 182190.##[2] K.C. Chattopadhyay, R.N. Hazra, and S.K. Samanta, Gradation of openness, Fuzzy Sets and Systems, 49 (1992), pp. 237242.##[3] K.C. Chattopadhyay and S.K. Samanta, Fuzzy topology, Fuzzy Sets and Systems, 54 (1993), pp. 207212. ##[4] Y.C. Kim, δclosure operators in fuzzy bitopological spaces, Far East J. Math. Sci., 2 (2000), pp. 791808. ##[5] Y.C. Kim, rfuzzy αopen and rfuzzy preopen sets in fuzzy bitopological spaces, Far East J. Math. Sci. Spec, (2000), pp. 315334.##[6] Y.C. Kim and S.E. Abbas, Several types of fuzzy regular spaces, Indian J. Pure and Appl. Math., 35 (2004), pp. 481500.##[7] Y.C. Kim and B. Krsteska, Fuzzy Pregular spaces, The Journal of Fuzzy Mathematics, 14 (2006), pp. 701722. ##[8] Y.C. Kim and J.W. Park, rfuzzy δclosure and rfuzzy θclosure sets, J. Korea Fuzzy Logic and Intelligent systems, 10 (2000), pp. 557563.##[9] Y.C. Kim, A.A. Ramadan, and S. E. Abbas rfuzzy strongly preopen sets in fuzzy topological spaces, Math. Vesnik, 55 (2003), pp. 113.##[10] T. Kubiak, On fuzzy topologies, Ph.D. Thesis, A. Mickiewicz, Poznan, 1985.##[11] A.A. Ramadan, Smooth topological spaces, Fuzzy Sets and Systems, 48 (1992), pp. 371375.##[12] D. Sobana, V. Chandrasekar, and A. Vadivel, Fuzzy econtinuity in Sostak's fuzzy topological spaces, (Submitted). ##[13] A.P. Sostak, Basic structures of fuzzy topology, J. Math. Sci., 78 (1996), pp. 662701.##[14] A.P. Sostak, Two decades of fuzzy topology: Basic ideas, Notion and results, Russian Math. Surveys, 44 (1989), pp. 125186. ##[15] A.P. Sostak, On a fuzzy topological structure, Rend. Circ. Matem. Palermo Ser II, 11 (1986), pp. 89103.##]