Some fixed point theorems in analysis

Singh, Kanhaya Lal (1968) Some fixed point theorems in analysis. 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 object of this thesis is to study the Contraction Mapping Principle given by Banach. The principle states: -- Theorem. Let f be a self mapping of a complete metric space X. -- If there exists a real number λ ε (0, 1) such that the condition -- d(f(x), f(y)) < λd(x, y) -- holds for every pair of points x, y ε X, then f has a unique fixed point. -- This theorem has been used extensively in proving existence and uniqueness theorems of differential and integral equations. Some examples have been given to illustrate its applications. -- Several generalizations of Banach's contraction principle have been given in recent years. We have tried to give some further generalizations in Chapter II. -- We have also studied Contractive mappings and Eventually contractive mappings. A few new results have been investigated related to these mappings. -- The converse statements of Banach's contraction principle have been given by a few mathematicians. We have also obtained a few new results on the converse of the Banach contraction principle. -- A few simple but interesting results related to commuting functions and common fixed points have been given. Some new results on commuting polynomials and common fixed points have been obtained.

Item Type: Thesis (Masters)
URI: http://research.library.mun.ca/id/eprint/7453
Item ID: 7453
Additional Information: Bibliography: leaves [124]-131.
Department(s): Science, Faculty of > Mathematics and Statistics
Date: 1968
Date Type: Submission
Library of Congress Subject Heading: Banach spaces

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