Measure of noncompactness, densifying mappings and fixed points

Riggio, Michele Ignazio (1972) Measure of noncompactness, densifying mappings and fixed points. 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 (4MB) [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 purpose of this thesis is to set forth some fixed point theorems in metric and Banach spaces for densifying mappings and k-set-contractions. -- In Chapter I, we discuss the Banach Contraction Principle and give an extensive coverage of its generalizations. Results are also given for contractive and nonexpansive mappings, and for mappings of an iterative type. -- In Chapter II, we introduce the concepts of α-measure (and X-measure) of noncompactness; some geometric properties are given. -- In Chapter III and IV we make a detailed study of some of the recent fixed point results in metric and Banach spaces respectively. -- Particular attention is given to the works of Furi, Vignoli, Nussbaum, and Petryshyn. -- In Chapter V, we give applications of α-measure to problems in optimization theory.

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