Norris, Carl Wallace (1969) Fixed and periodic points under contraction mappings in metric spaces. Masters thesis, Memorial University of Newfoundland.
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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)|
|Additional Information:||Bibliography: leaves 48-50.|
|Department(s):||Science, Faculty of > Mathematics and Statistics|
|Library of Congress Subject Heading:||Metric spaces; Fixed point theory|
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