Generalized hybrid mappings in Hilbert spaces and Banach spaces
type: Item
instance of: scholarly article
title: Generalized hybrid mappings in Hilbert spaces and Banach spaces
zbMATH Open document ID: 1277.47068
author: Ming-Hsiu Hsu
author: Wataru Takahashi
author: Jen-Chih Yao
published in: Taiwanese Journal of Mathematics
publication date: 2012-03-29T00:00:00Z
full work available at URL: http://journal.taiwanmathsoc.org.tw/index.php/TJM/article/view/1585
review text: Let \(C\) be a closed convex subset of a real Banach space \(X\) and \(\alpha,\beta\) be two real numbers. A mapping \(T:C\to C\) is called an \((\alpha,\beta)\)-generalized hybrid mapping if \(\alpha\|Tx-Ty\|^2+(1-\alpha)\|x-Ty\|^2\leq\beta\|Tx-y\|^2+(1-\beta)\|x-y\|^2\) for all \(x,y\in C\). Obviously, \((1,0)\)-, \((2,1)\)- and \((\frac32,\frac12)\)-generalized hybrid mappings are nonexpansive, nonspreading, and hybrid; and fixed point theorems for such mappings have been studied recently. In this paper, the authors prove fixed point theorems for \((\alpha,\beta)\)-generalized hybrid mappings and duality theorems for some nonlinear mappings.
reviewed by: Satit Saejung
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 6019751
zbMATH Keywords: Hilbert space
zbMATH Keywords: Banach space
zbMATH Keywords: nonexpansive mapping
zbMATH Keywords: nonspreading mapping
zbMATH Keywords: hybrid mapping
zbMATH Keywords: fixed point
MaRDI profile type: Publication
OpenAlex ID: W1855737895
DOI: 10.11650/TWJM/1500406532
description: scientific article; zbMATH DE number 6019751