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Metric Spaces: Including Fixed Point Theory and Set-valued Maps
Author(s): Qamrul Hasan Ansari

ISBN:    978-81-8487-099-2 
Publication Year:   2010
Pages:   208
Binding:   Paper Back
Dimension:   160mm x 240mm
Weight:   300


About the book

METRIC SPACES is intended for undergraduate students offering a course of metric spaces and post graduate students offering a course of nonlinear analysis or fixed point theory. The first six chapters cover basic concepts of metric spaces, separable spaces, compact spaces, connected spaces and continuity of functions defined on a metric space. Chapter seven is devoted to the metric fixed point theory. Banach contraction theorem and several of its generalizations along with their applications and Caristiís fixed point theorem are also given in this chapter. The introductory set-valued analysis with special emphysis on continuity and fixed point theory of set-valued maps is given in chapter eight. One of the most useful and important results from nonlinear analysis is Ekelandís variational principle. This principle along with several of its equivalent forms, Takahashiís minimization theorem, introduction of theory of equilibrium problems and the equilibrium version of Ekelandís variational principle and several of its equivalent forms are presented in the last chapter. This book will also be useful for researchers working in nonlinear analysis, optimization and theory of equilibrium problems.

Table of Contents

Preface / Notations and Abbreviations / Basic Concepts / Complete Metric Spaces / Separable Spaces / Compact Spaces / Continuous Functions / Connected Spaces / Fixed Point Theorems / Set-valued Maps / Ekelandís Variational Principle and its Applications / Some Basic Inequalities / Partial Ordering / Nested Interval Property / References / Index.


Undergraduate - Postgraduate Students and Researchers


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