Taiwanese Journal of Mathematics

STRONG CONVERGENCE TO COMMON FIXED POINTS OF A FINITE FAMILY OF ASYMPTOTICALLY NONEXPANSIVE MAP

Yonghong Yao and Yeong-Cheng Liou

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Abstract

Suppose $E$ is a real Banach space with uniform normal structure and suppose $E$ has a uniformly Gateaux differentiable norm. Let $C$ be a nonempty closed convex and bounded subset of $E$. Let $T_1,T_2,\cdots T_r: C \to C$ be a finite family of asymptotically nonexpansive mappings. In this paper, we suggest and analyze an iterative algorithm for a finite family of asymptotically nonexpansive mappings $\{T_i\}_{i=1}^r$. We show the convergence of the proposed algorithm to a common fixed point $p \in \cap_{i=1}^{r} F(T_i)$ which is the unique solution of some variational inequality. Our results can be considered as an refinement and improvement of many known results.

Article information

Source
Taiwanese J. Math., Volume 11, Number 3 (2007), 849-865.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500404761

Digital Object Identifier
doi:10.11650/twjm/1500404761

Mathematical Reviews number (MathSciNet)
MR2340167

Zentralblatt MATH identifier
1219.47135

Subjects
Primary: 47H05: Monotone operators and generalizations 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]

Keywords
asymptotically nonexpansive mapping common fixed point uniformly Gateaux differentiable norm strong convergence

Citation

Yao, Yonghong; Liou, Yeong-Cheng. STRONG CONVERGENCE TO COMMON FIXED POINTS OF A FINITE FAMILY OF ASYMPTOTICALLY NONEXPANSIVE MAP. Taiwanese J. Math. 11 (2007), no. 3, 849--865. doi:10.11650/twjm/1500404761. https://projecteuclid.org/euclid.twjm/1500404761


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