Fixed point theorems for a sum of two mappings in locally convex spaces
type: Item
instance of: scholarly article
title: Fixed point theorems for a sum of two mappings in locally convex spaces
zbMATH Open document ID: 0805.47057
DOI: 10.1155/S0161171294000967
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1995-02-05T00:00:00Z
full work available at URL: https://eudml.org/doc/47057
review text: Summary: Cain and Nashed generalized to locally convex spaces a well known fixed point theorem of Krasnosel'skij for a sum of contraction and compact mappings in Banach spaces. The class of asymptotically nonexpansive mappings includes properly the class of nonexpansive mappings as well as the class of contraction mappings. In this paper, we prove by using the same method some results concerning the existence of fixed points for a sum of nonexpansive and continuous mappings and also a sum of asymptotically nonexpansive and continuous mappings in locally convex spaces. These results extend a result of Cain and Nashed.
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 54H25
zbMATH DE Number: 697107
zbMATH Keywords: uniformly asymptotically regular with respect to a map
zbMATH Keywords: fixed point theorem of Krasnosel'skij for a sum of contraction and compact mappings in Banach spaces
zbMATH Keywords: asymptotically nonexpansive mappings
zbMATH Keywords: sum of asymptotically nonexpansive and continuous mappings in locally convex spaces
author: Palaniappan Vijayaraju
MaRDI profile type: Publication
OpenAlex ID: W1995862661
description: scientific article; zbMATH DE number 697107