Thakur's Iterative Scheme for Approximating Common Fixed Points to a Pair of Relatively Nonexpansive Mappings

被引：3
作者：
Gopi, R. [1 ]
Pragadeeswarar, V. [2 ]
De la Sen, M. [3 ]
机构：
[1] Presidency Univ, Sch Engn, Dept Math, Bangalore, Karnataka, India
[2] Amrita Vishwa Vidyapeetham, Amrita Sch Engn, Dept Math, Coimbatore, Tamil Nadu, India
[3] Univ Basque Country, Inst Res & Dev Proc IIDP, Campus Leioa,POB 48940, Leioa, Bizkaia, Spain
来源：
JOURNAL OF MATHEMATICS | 2022年 / 2022卷
关键词：
CONVERGENCE;
D O I：
10.1155/2022/5537768
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this work, we propose the three-step Takur iterative process associated with two mappings in the setting of Banach space. Using this Takur iteration, we approximate a common fixed point for a pair of noncyclic, relatively nonexpansive mappings. And we support our main result with a numerical example. Also, we give a stronger version of our main result by using von Neumann sequences. Finally, we provide some corollaries on the convergence of common best proximity points in uniformly convex Banach space.
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页数：16
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共 27 条
  • [1] Approximation of Fixed Points and Best Proximity Points of Relatively Nonexpansive Mappings
    Abdeljawad, Thabet
    Ullah, Kifayat
    Ahmad, Junaid
    De La Sen, Manuel
    Ulhaq, Azhar
    [J]. JOURNAL OF MATHEMATICS, 2020, 2020
  • [2] Global Optimal Solutions of Noncyclic Mappings in Metric Spaces
    Abkar, A.
    Gabeleh, M.
    [J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2012, 153 (02) : 298 - 305
  • [3] Agarwal RP, 2007, J NONLINEAR CONVEX A, V8, P61
  • [4] Bauschke H.H., 1993, SetValued Analysis, V1, P185, DOI DOI 10.1007/BF01027691
  • [5] NONEXPANSIVE NONLINEAR OPERATORS IN A BANACH SPACE
    BROWDER, FE
    [J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1965, 54 (04) : 1041 - &
  • [6] Chidume C, 2009, LECT NOTES MATH, V1965, P1
  • [7] Ciric Lj.B., 2003, Archivum Mathematicum, V39, P123
  • [8] Existence and convergence of best proximity points
    Eldred, A. Anthony
    Veeramani, P.
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 323 (02) : 1001 - 1006
  • [9] CONVERGENCE OF MANN'S ITERATION FOR RELATIVELY NONEXPANSIVE MAPPINGS
    Eldred, A. Anthony
    Praveen, A.
    [J]. FIXED POINT THEORY, 2017, 18 (02): : 545 - 554
  • [10] Proximal normal structure and relatively nonexpansive mappings
    Eldred, AA
    Kirk, WA
    Veeramani, P
    [J]. STUDIA MATHEMATICA, 2005, 171 (03) : 283 - 293
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