Fixed point theorems in metric spaces and applications

Cheema, Pritam Singh (1971) Fixed point theorems in metric spaces and applications. 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 (1MB) [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 object of this thesis is to study the fixed point theorems under contraction and contractive mappings in metric spaces. -- We have discussed the Banach's contraction principle, "A contraction mapping of a complete metric space into itself has a unique fixed point", together with its various generalizations in metric spaces. -- A few new results which guarantee the existence and uniqueness of fixed points for contraction, contractive mappings and mappings with a contractive iterate have been given for metric spaces. -- An attempt has been made to give more general theorems for mappings of the form d(Tx,Ty) ≤ ψ(d(x,y)) on metric spaces. A few fixed point theorems on generalized metric space have been obtained. -- In the end, some applications of the fixed point theorems are illustrated by taking suitable examples.

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