FIBONACCI-MANN ITERATION FOR MONOTONE ASYMPTOTICALLY NONEXPANSIVE MAPPINGS

被引：16

作者：

Alfuraidan, M. R. ^{[1
]}

Khamsi, M. A. ^{[2
]}

机构：

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

[2] Univ Texas El Paso, Dept Math Sci, El Paso, TX 79968 USA

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2017年 / 96卷 / 02期

关键词：

asymptotically nonexpansive mapping; Fibonacci sequence; fixed point; Mann iteration process; monotone Lipschitzian mapping; Opial condition; uniformly convex Banach space; FIXED-POINT THEOREM;

D O I：

10.1017/S0004972717000120

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We extend the results of Schu ['Iterative construction of fixed points of asymptotically nonexpansive mappings', J. Math. Anal. Appl. 158 (1991), 407-413] to monotone asymptotically nonexpansive mappings by means of the Fibonacci-Mann iteration process x(n+1) = t(n)T(f(n))(x(n)) + (1 - t(n))x(n), n is an element of N, where T is a monotone asymptotically nonexpansive self-mapping defined on a closed bounded and nonempty convex subset of a uniformly convex Banach space and {f (n)} g is the Fibonacci integer sequence. We obtain a weak convergence result in L-p([0; 1]), with 1 < p < +infinity, using a property similar to the weak Opial condition satisfied by monotone sequences.

引用

页码：307 / 316

页数：10

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