Fixed point theorems and convergence theorems for generalized nonspreading mappings in Banach spaces
type: Item
instance of: scholarly article
title: Fixed point theorems and convergence theorems for generalized nonspreading mappings in Banach spaces
zbMATH Open document ID: 1286.47036
author: Ngai-Ching Wong
author: Jen-Chih Yao
author: Wataru Takahashi
published in: Journal of Fixed Point Theory and Applications
publication date: 2012-12-05T00:00:00Z
review text: The authors deal with the class of \(2\)-generalized nonspreading mappings which is one of the three classes of nonlinear mappings defined in the authors' paper [J. Nonlinear Convex Anal. 13, No.~2, 363--381 (2012; Zbl 1248.47056)] in Banach spaces. They first prove a general fixed point theorem for nonlinear mappings in a Banach space. Using this result, the authors give another proof of their earlier fixed point theorem [loc.\,cit.]\ for 2-generalized nonspreading mappings in Banach spaces. Then they prove a nonlinear mean convergence theorem of \textit{J.-B. Baillon}'s type [C. R. Acad. Sci., Paris, Sér. A 280, 1511--1514 (1975; Zbl 0307.47006)] and a weak convergence theorem of \textit{W. R. Mann}'s type [Proc. Am. Math. Soc. 4, 506--510 (1953; Zbl 0050.11603)] for such nonlinear mappings in a Banach space.
reviewed by: Shahram Saeidi
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H05
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 6112752
zbMATH Keywords: Banach space
zbMATH Keywords: nonexpansive mapping
zbMATH Keywords: nonspreading mapping
zbMATH Keywords: hybrid mapping
zbMATH Keywords: fixed point
MaRDI profile type: Publication
full work available at URL: s11784-012-0074-3
OpenAlex ID: W1980868753
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DOI: 10.1007/S11784-012-0074-3
description: scientific article; zbMATH DE number 6112752