Non-expansive mappings and fixed points in metric spaces

Dube, Lakshmi Shankar (1970) Non-expansive mappings and fixed points in metric spaces. Masters thesis, Memorial University of Newfoundland.

[English] PDF (Migrated (PDF/A Conversion) from original format: (application/pdf)) - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. Download (6MB) [English] PDF - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. (Original Version)

Abstract

The main objective of this thesis is to investigate fixed points under non-expansive and some other types of mappings in metric spaces. During the course of this dissertation, several new results have been obtained. In order to illustrate some of the theorems proved, a few interesting examples have been constructed. -- Chapter I includes a brief survey of fixed point theorems for non-expansive mappings. In the end a few theorems, which seem to be new, have been added. -- In Chapter II, a mapping considered by Kannan [20]has been observed and by introducing some more general forms of this mapping, a few interesting results on fixed points have been investigated. Furthermore, giving a brief account of multi-valued contraction mappings and their fixed points, a search for extending some fixed point theorems to their multivalued analogues has been made. -- Chapter III deals with the convergence of sequence of mappings (contraction and Kannan type) and their fixed points. A few interesting generalizations of some known results have been investigated.

Actions (login required)

View Item