University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
17
2
2020
06
01
A New Iterative Algorithm for Multivalued Nonexpansive Mappping and Equlibruim Problems with Applications
1
22
EN
Thierno Mohadamane Mansour
Sow
Gaston Berger University, Saint Louis, Senegal.
sowthierno89@gmail.com
10.22130/scma.2019.93964.499
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
https://scma.maragheh.ac.ir/article_37371.html
https://scma.maragheh.ac.ir/article_37371_a45543e6139e50592742c377bbb3e07a.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
17
2
2020
06
01
Fixed Point Theorems on Complete Quasi Metric Spaces Via C-class and A-Class Functions
23
36
EN
Mensur
Yalcin
Department of Mathematics, Faculty of Science and Arts, Kirikkale University, 71450 Yahsihan, Kirikkale, Turkey.
tuugbaa@hotmail.co
Hakan
Simsek
Department of Mathematics, Faculty of Science and Arts, Kirikkale University, 71450 Yahsihan, Kirikkale, Turkey.
hasimsek@hotmail.com
Ishak
Altun
Department of Mathematics, Faculty of Science and Arts, Kirikkale University, 71450 Yahsihan, Kirikkale, Turkey.
ishakaltun@yahoo.com
10.22130/scma.2019.97961.527
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
https://scma.maragheh.ac.ir/article_37373.html
https://scma.maragheh.ac.ir/article_37373_a6570a8c7efa8102a5a2376c2d3d7fd4.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
17
2
2020
06
01
Some Fixed Point Theorems in Generalized Metric Spaces Endowed with Vector-valued Metrics and Application in Linear and Nonlinear Matrix Equations
37
53
EN
Hasan
Hosseinzadeh
0000-0002-1723-4140
Department of Mathematics, Ardabil Branch, Islamic Azad University, Ardabil, Iran.
hasan_hz2003@yahoo.com
10.22130/scma.2018.86797.440
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
https://scma.maragheh.ac.ir/article_37410.html
https://scma.maragheh.ac.ir/article_37410_f2d64a18e13a8179dcb9e3507cf25af1.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
17
2
2020
06
01
Some Results on the Field of Values of Matrix Polynomials
55
68
EN
Zahra
Boor Boor Azimi
Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran.
zahraazimi1@gmail.com
Gholamreza
Aghamollaei
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman,
Kerman, Iran.
aghamollaei@uk.ac.ir
10.22130/scma.2018.88329.461
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
https://scma.maragheh.ac.ir/article_37411.html
https://scma.maragheh.ac.ir/article_37411_9e2b73b28530ee677702cc376d967792.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
17
2
2020
06
01
Vector Optimization Problems and Generalized Vector Variational-Like Inequalities
69
82
EN
Ildar
Sadeqi
Department of Mathematics, Sahand University of Technology, Tabriz, Iran.
esadeqi@sut.ac.ir
Somayeh
Nadi
Department of Mathematics, Sahand University of Technology, Tabriz, Iran.
s.nadi229@gmail.com
10.22130/scma.2018.85895.433
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
https://scma.maragheh.ac.ir/article_37712.html
https://scma.maragheh.ac.ir/article_37712_612932aa8853c744edc12091035d112c.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
17
2
2020
06
01
Common Fixed Point Results on Complex-Valued $S$-Metric Spaces
83
105
EN
Nihal
Taş
0000-0002-4535-4019
Department of Mathematics, Bali kesir University, 10145, Bali kesir, Turkey.
nihalarabacioglu@hotmail.com
Nihal
Yilmaz Ozgur
0000-0002-8152-1830
Department of Mathematics, Bal\i kesir University, 10145 Bal\i kesir, Turkey.
nyozgur@gmail.com
10.22130/scma.2018.92986.488
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 fixed<br />point theorems.
$S$-metric space,Fixed point theorem,Common fixed point theorem,Complex valued $S$-metric space
https://scma.maragheh.ac.ir/article_37412.html
https://scma.maragheh.ac.ir/article_37412_b6d9f7287f605b0fe1bd1bc28da3845b.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
17
2
2020
06
01
On the Monotone Mappings in CAT(0) Spaces
107
117
EN
Davood
Afkhami Taba
Department of Mathematics, Bandar Abbas Branch, Islamic Azad University, P.O.Box 79158-93144, Bandar Abbas, Iran.
afkhami420@yahoo.com
Hossein
Dehghan
Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Gava Zang, P.O.Box 45137-66731, Zanjan, Iran
hossein.dehgan@gmail.com
10.22130/scma.2019.69719.273
In this paper, we first introduce a monotone mapping and its resolvent in general metric spaces.<br />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
https://scma.maragheh.ac.ir/article_37414.html
https://scma.maragheh.ac.ir/article_37414_32c80ecebc2c3d6c8e60ea1c74bfbb9a.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
17
2
2020
06
01
Best Proximity Point Results for Almost Contraction and Application to Nonlinear Differential Equation
119
138
EN
Azhar
Hussain
Department of Mathematics, University of Sargodha, Sargodha-40100, Pakistan.
hafiziqbal30@yahoo.com
Mujahid
Abbas
Department of Mathematics, Government College University, Lahore 54000, Pakistan and Department of Mathematics and Applied Mathematics, University of Pretoria Hatfield 002, Pretoria, South Africa.
abbas.mujahid@gmail.com
Muhammad
Adeel
Department of Mathematics, University of Sargodha, Sargodha-40100, Pakistan.
adeel.uosmaths@gmail.com
Tanzeela
Kanwal
Department of Mathematics, University of Sargodha, Sargodha-40100, Pakistan.
tanzeelakanwal16@gmail.com
10.22130/scma.2019.95982.515
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 and<br />to 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
https://scma.maragheh.ac.ir/article_38391.html
https://scma.maragheh.ac.ir/article_38391_8add387ec1b4cd717b79ca1c2b06cf11.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
17
2
2020
06
01
Inequalities of Ando's Type for $n$-convex Functions
139
159
EN
Rozarija
Mikic
University of Zagreb, Faculty of Textile Technology, 10000 Zagreb, Croatia.
rozarija.jaksic@ttf.hr
Josip
Pečarić
RUDN University, Miklukho-Maklaya str. 6, 117198 Moscow, Russia.
pecaric@element.hr
10.22130/scma.2018.94775.506
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
https://scma.maragheh.ac.ir/article_37469.html
https://scma.maragheh.ac.ir/article_37469_2d7ac926af76cbb8dedb6c7e2dfbdd48.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
17
2
2020
06
01
New Generalization of Darbo's Fixed Point Theorem via $alpha$-admissible Simulation Functions with Application
161
171
EN
Hossein
Monfared
Department of Mathematics, Bilehsavar Branch, Islamic Azad University, Bilehsavar, Iran.
monfared.h@gmail.com
Mehdi
Asadi
Department of Mathematics, Zanjan Branch, Islamic Azad University, Zanjan, Iran.
masadi.azu@gmail.com
Ali
Farajzadeh
0000-0001-5221-6741
Department of Mathematics, Razi University, Kermanshah, 67149, Iran.
farajzadehali@gmail.com
10.22130/scma.2018.84950.427
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
https://scma.maragheh.ac.ir/article_37836.html
https://scma.maragheh.ac.ir/article_37836_39ad1aa7de0c747d55d528d05434e30a.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
17
2
2020
06
01
Bornological Completion of Locally Convex Cones
173
183
EN
Davood
Ayaseh
0000-0002-9225-319x
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
d_ayaseh@tabrizu.ac.ir
Asghar
Ranjbari
0000-0003-0789-4812
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
ranjbari@tabrizu.ac.ir
10.22130/scma.2019.107061.601
In this paper, firstly, we obtain some new results about bornological convergence in locally convex cones (which was studied in [1]) 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
https://scma.maragheh.ac.ir/article_39051.html
https://scma.maragheh.ac.ir/article_39051_d288ff89dcc9ff1cf567e425be3f5c8f.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
17
2
2020
06
01
Generalized Continuous Frames for Operators
185
201
EN
Chander
.Shekhar
Department of Mathematics Indraprastha college for Women, University of Delhi, Delhi 110054, India.
shekhar.hilbert@gmail.com
Sunayana
Bhati
Department of Mathematics and Statistics, University college of Science, M.L.S. University, Udaipur, Rajasthan, India.
bhatisunayana@gmail.com
G.S.
Rathore
Department of Mathematics and Statistics, University college of Science, M.L.S. University, Udaipur, Rajasthan, India.
ghanshyamsrathore@yahoo.co.in
10.22130/scma.2018.97329.523
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
https://scma.maragheh.ac.ir/article_37409.html
https://scma.maragheh.ac.ir/article_37409_6c5ddb5008c0e3934c7fff932837d13d.pdf