Robertson, Arthur Joseph Lewis (1976) On the convergence of the sequence of iterates. Masters thesis, Memorial University of Newfoundland.
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The main objective of this thesis is to study the convergence of sequences of various iterates to a fixed point in certain Banach spaces. -- The preliminaries of metric spaces, normed linear spaces, and basic fixed point concepts are covered in the first chapter. -- In the second chapter, the first section gives a brief statement of the problem of convergence of sequences of iterates. -- The second section traces the development of some of the more important results on the convergence of sequences of iterates. The concept of a densifying mapping is then introduced and a similar development of theorems for these mappings is given. -- The last section covers a more general sequence of iterates. An extension of a theorem by Senter  is presented and a corrected version of his original theorem is given. The corrected version is then shown to be a corollary of the new theorem. It is also shown that a condition Z of Rhoades  is a subset of one of the conditions of the new theorem. The final theorem in this section is an extension of one by Petryshyn and Williamson  to this more general sequence of iterates.
|Item Type:||Thesis (Masters)|
|Additional Information:||Bibliography: leaves 44-45.|
|Department(s):||Science, Faculty of > Mathematics and Statistics|
|Library of Congress Subject Heading:||Convergence; Banach spaces|
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