# Iterated contraction mappings and fixed point theorems in metric spaces

Hynes, Frank (1972) Iterated contraction mappings and fixed point theorems in metric spaces. Masters thesis, Memorial University of Newfoundland.

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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.

•  [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 fixed point theorems for iterated contraction mappings in metric and generalized metric spaces. -- In the beginning, we have discussed 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. -- Then the iterated contraction mapping, “d(Tx,TTx) ≤ kd(x,Tx), for all x, Tx E (X,d), T : X – X, and for some constant k, 0 ≤ k < 1", has been considered. We have given the iterated contraction mapping principle, "An iterated contraction mapping, which is continuous at the limit of its sequence of iterates, of a complete metric space into itself has a fixed point", by following the procedure of the Banach Contraction Principle. Then generalizations of the iterated contraction principle have been given in metric spaces. Iterated contractive mappings, "d(Tx,TTx) < d(x,Tx), for all x, Tx E (X,d), x = Tx, T : X – X” and iterated nonexpansive mappings, “d(Tx,TTx) ≤ d(x,Tx), for all x, Tx E (X,d), T : X – X”, have also been considered briefly in metric spaces. -- In the end, we have given the results on iterated contraction mappings in generalized metric spaces.

Item Type: Thesis (Masters) http://research.library.mun.ca/id/eprint/1098 1098 Bibliography: leaves 66-70. Science, Faculty of > Mathematics and Statistics 1972 Submission Metric spaces

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