Fixed and periodic points under contraction mappings in metric spaces

Norris, Carl Wallace (1969) Fixed and periodic points under contraction mappings 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.
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Abstract

The main aim of this thesis is to investigate fixed and periodic points under contraction or distance shrinking mappings in metric spaces. -- Various situations are explored where the notion of contraction is relaxed and suitable modifications made on the metric space to ensure fixed or periodic points for the contraction. -- During the course of these investigations a few new results which guarantee fixed or periodic points for contractions under suitably weak conditions have been given for metric spaces. -- A few fixed point theorems have been also given in generalized complete metric spaces. Some of these are generalizations of well known results in this space. -- Convergence of a sequence of contractions and their fixed points have been studied briefly and a few new theorems have been added. -- In the end an attempt is made to apply the contraction mapping principle to the theory of differential and integral equations.

Item Type: Thesis (Masters)
URI: http://research.library.mun.ca/id/eprint/7235
Item ID: 7235
Additional Information: Bibliography: leaves 48-50.
Department(s): Science, Faculty of > Mathematics and Statistics
Date: 1969
Date Type: Submission
Library of Congress Subject Heading: Metric spaces; Fixed point theory

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