Weak Convergence Theorems for Nonself Mappings

Weak Convergence Theorems for Nonself Mappings

Year:    2015

Author:    Yongquan Liu, Weiping Guo

Communications in Mathematical Research , Vol. 31 (2015), Iss. 1 : pp. 15–22

Abstract

Let $E$ be a real uniformly convex and smooth Banach space, and $K$ be a nonempty closed convex subset of $E$ with $P$ as a sunny nonexpansive retraction. Let $T_1, T_2 : K → E$ be two weakly inward nonself asymptotically nonexpansive mappings with respect to P with a sequence $\{k^{(i)}_n\} ⊂ [1, ∞) (i = 1, 2)$, and $F := F(T_1) ∩ F(T_2) ≠ ∅$. An iterative sequence for approximation common fixed points of the two nonself asymptotically nonexpansive mappings is discussed. If $E$ also has a Fréchet differentiable norm or its dual $E^∗$ has Kadec-Klee property, then weak convergence theorems are obtained.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.13447/j.1674-5647.2015.01.02

Communications in Mathematical Research , Vol. 31 (2015), Iss. 1 : pp. 15–22

Published online:    2015-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    8

Keywords:    asymptotically nonexpansive nonself-mapping weak convergence uniformly convex Banach space common fixed point smooth Banach space.

Author Details

Yongquan Liu

Weiping Guo