Geometry of Banach spaces and some fixed point theorems

Yadav, Raj Kishore (1972) Geometry of Banach spaces and some fixed point theorems. 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 aim of this thesis is to study the geometry of Banach spaces, the existence of fixed points and the convergence of iterative sequences of certain mappings in Banach spaces. -- We introduce some of the basic definitions and give a brief survey of some well-known results on fixed points for different mappings. -- We also introduce and discuss different classifications of Banach spaces. A few results, similar to those of uniformly convex Banach spaces, have been given for weakly uniformly convex and weakly* uniformly convex Banach spaces. -- Finally considering more general mappings, of types Diaz and Metcalf [46], Dotson [48], Kirk [87], some new results and various generalizations have been given on the asymptotic regularity and the convergence of the iterative sequences in Banach spaces. We end with mentioning some of the applications of fixed point theory in brief.

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