Approximating common fixed points of total asymptotically nonexpansive mappings in CAT(0) spaces

被引：5

作者：

Fukhar-ud-din, Hafiz ^{[1
]}

Khan, Abdul Rahim ^{[1
]}

Hussain, Nawab ^{[2
]}

机构：

[1] King Fahd Univ Petr & Minerals, Dept Math & Stat, Dhahran 31261, Saudi Arabia

[2] King Abdulaziz Univ, Dept Math, POB 80203, Jeddah 21589, Saudi Arabia

来源：

JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS | 2017年 / 10卷 / 02期

关键词：

CAT (0) space; total asymptotically nonexpansive mapping; one-step iterative algorithm; common fixed point; Delta-convergence; strong convergence; DELTA-CONVERGENCE THEOREMS; ITERATION;

D O I：

10.22436/jnsa.010.02.37

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce and study convergence of a one-step iterative algorithm for a finite family of total asymptotically nonexpansive mappings on a CAT(0) space. Our results are new in Hilbert spaces as well as CAT(0) spaces; in particular, an analogue of Rhoades weak convergence theorem [B. E. Rhoades, Bull. Austral. Math. Soc., 62 (2000), 307-310] is established both for Delta-convergence and strong convergence in CAT(0) spaces. (C) 2017 All rights reserved.

引用

页码：771 / 779

页数：9

共 24 条

[1] A New One-Step Iterative Process for Common Fixed Points in Banach Spaces [J].

Abbas, Mujahid ;

Khan, Safeer Hussain ;

Kim, Jong Kyu .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2008, 2008 (1)

[2]

Abbas M, 2011, HACET J MATH STAT, V40, P563

[3] Approximating fixed points of total asymptotically nonexpansive mappings [J].

Alber, Ya. I. ;

Chidume, C. E. ;

Zegeye, H. .

FIXED POINT THEORY AND APPLICATIONS, 2006, 2006 (1)

[4] Convergence comparison and stability of Jungck-Kirk-type algorithms for common fixed point problems [J].

Alotaibi, Abdullah ;

Kumar, Vivek ;

Hussain, Nawab .

FIXED POINT THEORY AND APPLICATIONS, 2013,

[5]

Bridson MR., 1999, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], V319, P1

[6]

Chidume C. E., 2014, ABSTR APPL AN, V2014

[7] On Kirk's strong convergence theorem for multivalued nonexpansive mappings on CAT(0) spaces [J].

Dhompongsa, S. ;

Kaewkhao, A. ;

Panyanak, B. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (02) :459-468

[8] On Δ-convergence theorems in CAT(0) spaces [J].

Dhompongsa, S. ;

Panyanak, B. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 56 (10) :2572-2579

[9]

Fukhar-Ud-Din H, 2014, CARPATHIAN J MATH, V30, P175

[10] FIXED-POINT THEOREM FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS [J].

GOEBEL, K ;

KIRK, WA .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 35 (01) :171-&

← 1 2 3 →