STRONG CONVERGENCE OF HALPERN'S TYPE ITERATION FOR α-NONEXPANSIVE SEMIGROUP IN BANACH SPACES AND CAT(0) SPACES

被引：0

作者：

Oyetunbi, Dolapo Muhammed ^{[1
]}

Khan, Abdul Rahim ^{[2
]}

机构：

[1] Univ Ottawa, Dept Math & Stat, Ottawa, ON, Canada

[2] Inst Southern Punjab, Dept Math & Stat, Multan, Pakistan

来源：

FIXED POINT THEORY | 2024年 / 25卷 / 01期

关键词：

Semigroup; alpha-nonexpansive mapping; common fixed point; Banach space; CAT(0) space; COMMON FIXED-POINTS; DELTA-CONVERGENCE; MAPPINGS; THEOREMS; APPROXIMATION;

D O I：

10.24193/fpt-ro.2025.1.17

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we establish strong convergence of the Halpern's type iteration for a semigroup of alpha-nonexpansive mappings in Banach spaces. Using the concept of quasilinearization, we extend this result to CAT (0) spaces, an important subclass of metric spaces. Our work generalizes and complements several comparable results existing in the literature.

引用

页码：271 / 288

页数：18

共 32 条

[1]

Aleyner A, 2005, J NONLINEAR CONVEX A, V6, P137

[2] Fixed point theorem for α-nonexpansive mappings in Banach spaces [J].

Aoyama, Koji ;

Kohsaka, Fumiaki .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (13) :4387-4391

[3]

Ariza-Ruiz D, 2016, CARPATHIAN J MATH, V32, P13

[4] Construction of sunny nonexpansive retractions in Banach spaces [J].

Benavides, TD ;

López-Acedo, G ;

Xu, HK .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2002, 66 (01) :9-16

[5] Quasilinearization and curvature of Aleksandrov spaces [J].

Berg, I. D. ;

Nikolaev, I. G. .

GEOMETRIAE DEDICATA, 2008, 133 (01) :195-218

[6]

BRUHAT F, 1972, PUBL MATH-PARIS, V41, P5

[7] Approximation of fixed points of pseudocontraction semigroups based on a viscosity iterative process [J].

Cho, Sun Young ;

Kang, Shin Min .

APPLIED MATHEMATICS LETTERS, 2011, 24 (02) :224-228

[8] Convergence theorems for nonexpansive semigroups in CAT(0) spaces [J].

Cho, Yeol Je ;

Ciric, Ljubomir ;

Wang, Sheng-hua .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (17) :6050-6059

[9]

Dehghan H., 2012, ICFGA 2012, P41

[10] A weak convergence theorem for common fixed points of some generalized nonexpansive mappings and nonspreading mappings in a Hilbert space [J].

Dhompongsa, S. ;

Inthakon, W. ;

Takahashi, W. .

OPTIMIZATION, 2011, 60 (06) :769-779

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