Random fixed point theorems for various classes of 1-set-contractive maps in Banach spaces
type: Item
instance of: scholarly article
title: Random fixed point theorems for various classes of 1-set-contractive maps in Banach spaces
zbMATH Open document ID: 0893.47037
author: Nazeer Shahzad
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-08-24T00:00:00Z
review text: The author proves a random fixed point theorem for 1-set contractive random operators (of course satisfying certain conditions). Most random fixed point theorems proved earlier deal with condensing or nonexpansive random operators. The class of 1-set contractive operator includes condensing, nonexpansive, semicontractive type and locally almost nonexpansive random operators. By using the main theorem, some random fixed point theorems have been deduced for various special classes of random operators mentioned. To prove the main theorem, results of \textit{H. Xu} [Proc. Am. Math. Soc. 110, No. 2, 395-400 (1990; Zbl 0716.47029)] and of \textit{K.-K. Tan} and \textit{X.-Z. Yuan} [J. Math. Anal. Appl. 185, No. 2, 378-390 (1994; Zbl 0856.47036)] have been used. The author has generalized or extended results obtained by \textit{S. Itoh} [J. Math. Anal. Appl. 67, 261-273 (1979; Zbl 0407.60069)], \textit{T.-C. Lin} [Proc. Am. Math. Soc. 103, No. 4, 1129-1135 (1988; Zbl 0676.47041); ibid. 123, No. 4, 1167-1176 (1993; Zbl 0834.47049)] and Xu mentioned above.
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H40
Mathematics Subject Classification ID: 60H25
zbMATH DE Number: 954708
zbMATH Keywords: weakly inward map
zbMATH Keywords: Leray-Schauder condition
zbMATH Keywords: 1-set contractive random operators
zbMATH Keywords: random fixed point theorems
zbMATH Keywords: semicontractive type
reviewed by: R. K. Bose
MaRDI profile type: Publication
OpenAlex ID: W2031659000
DOI: 10.1006/JMAA.1996.0407
description: scientific article; zbMATH DE number 954708