Monotone Orbitally Nonexpansive and Cyclic Mappings in Partially Ordered Uniformly Convex Banach Spaces

被引：0

作者：

Gabeleh, Moosa ^{[1
]}

Karimi, Lotfollah ^{[2
]}

Vetro, Calogero ^{[3
]}

机构：

[1] Ayatollah Boroujerdi Univ, Dept Math, Boroujerd, Iran

[2] Hamedan Univ Technol, Dept Elect Engn, Hamadan, Iran

[3] Univ Palermo, Dept Math & Comp Sci, Via Archirafi 34, I-90123 Palermo, Italy

来源：

IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS | 2024年 / 19卷 / 01期

关键词：

Best proximity point; T-cyclic contraction; Monotone orbitally nonexpansive mapping; Uniformly convex Banach space; FIXED-POINT THEOREM; CONVERGENCE;

D O I：

10.61186/ijmsi.19.1.19

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the setting of uniformly convex Banach spaces equipped with a partially ordered relation, we survey the existence of fixed points for monotone orbitally nonexpansive mappings. In this way, we extend and improve the main results of Alfuraidan and Khamsi [M. R. Alfuraidan, M. A. Khamsi, Proc. Amer. Math. Soc. , 146 , (2018), 2451-2456]. Examples are given to show the usability of our main conclusions. We also study the existence of an optimal solution for cyclic contractions in such spaces.

引用

页码：19 / 33

页数：15

共 50 条

[31] Common fixed points for some generalized nonexpansive mappings and nonspreading-type mappings in uniformly convex Banach spaces
Warunun Inthakon
Attapol Kaewkhao
Nutchari Niyamosot
[J]. Fixed Point Theory and Applications, 2012
[32] Pointwise Lipschitzian mappings in uniformly convex and uniformly smooth Banach spaces
Kozlowski, W. M.
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2013, 84 : 50 - 60
[33] Convergence of three-step iterations for total asymptotically nonexpansive mappings in uniformly convex Banach spaces
Zuo, Zhanfei
[J]. SCIENCEASIA, 2014, 40 (04): : 301 - 305
[34] NEW ITERATIVE SCHEME FOR THE APPROXIMATION OF FIXED POINTS OF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS IN UNIFORMLY CONVEX BANACH SPACES
Kang, Shin Min
Rafiq, Arif
Kwun, Young Chel
Ali, Faisal
[J]. JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, 2015, 19 (02) : 287 - 297
[35] Convergence Theorems for Infinite Family of Multivalued Quasi-Nonexpansive Mappings in Uniformly Convex Banach Spaces
Bunyawat, Aunyarat
Suantai, Suthep
[J]. ABSTRACT AND APPLIED ANALYSIS, 2012,
[36] CYCLIC RELATIVELY NONEXPANSIVE MAPPINGS IN CONVEX METRIC SPACES
Gabeleh, Moosa
[J]. MISKOLC MATHEMATICAL NOTES, 2015, 16 (01) : 133 - 144
[37] GENERALIZED NONEXPANSIVE MULTIVALUED MAPPINGS IN STRICTLY CONVEX BANACH SPACES
Abkar, Ali
Eslamian, Mohammad
[J]. FIXED POINT THEORY, 2013, 14 (02): : 269 - 280
[38] Properties of Fixed Point Sets of Monotone Nonexpansive Mappings in Banach Spaces
Bachar, Mostafa
Khamsi, Mohamed A.
[J]. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2016, 37 (03) : 277 - 283
[39] A monotone hybrid algorithm for a family of generalized nonexpansive mappings in Banach spaces
Alizadeh, Sattar
Moradlou, Fridoun
[J]. INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, 2022, 13 (02): : 2347 - 2359
[40] On convergence of iteration processes for nonexpansive semigroups in uniformly convex and uniformly smooth Banach spaces
Kozlowski, Wojciech M.
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 426 (02) : 1182 - 1191

← 1 2 3 4 5 →