Fixed Point Theory for Lipschitzian-Type Mappings with Applications

By: Ravi P. Agarwal, Donal O'Regan, D. R. Sahu

Write A Review

Hardcover | 27 May 2009

At a Glance

Hardcover
380 Pages

Dimensions(cm)
23.39 x 15.6 x 2.24

Hardcover

RRP $249.00

$123.40

50%OFF

or 4 interest-free payments of $30.85 with

or

Aims to ship in 15 to 25 business days

In recent years, the fixed point theory of Lipschitzian-type mappings has rapidly grown into an important field of study in both pure and applied mathematics. It has become one of the most essential tools in nonlinear functional analysis.

This self-contained book provides the first systematic presentation of Lipschitzian-type mappings in metric and Banach spaces. The first chapter covers some basic properties of metric and Banach spaces. Geometric considerations of underlying spaces play a prominent role in developing and understanding the theory. The next two chapters provide background in terms of convexity, smoothness and geometric coefficients of Banach spaces including duality mappings and metric projection mappings. This is followed by results on existence of fixed points, approximation of fixed points by iterative methods and strong convergence theorems. The final chapter explores several applicable problems arising in related fields.

This book can be used as a textbook and as a reference for graduate students, researchers and applied mathematicians working in nonlinear functional analysis, operator theory, approximations by iteration theory, convexity and related geometric topics, and best approximation theory.

Industry Reviews

From the reviews: "The present book explains many of the basic techniques and ... the classical results of fixed point theory, and normal structure properties. ... Exercises are included in each chapter. As such, it is a self-contained book that can be used in a course for graduate students." (Srinivasa Swaminathan, Zentralblatt MATH, Vol. 1176, 2010) "This book provides a presentation of fixed point theory for Lipschitzian type mappings in metric and Banach spaces. ... An exercise section is included at the end of each chapter, containing interesting and well chosen material in order to cover topics complementing the main body of the text. ... It is worthwhile to point out that a beginner in this area is certainly well served with this text ... . A book including all ... topics together for sure should be welcomed for graduate students." (Enrique Llorens-Fuster, Mathematical Reviews, Issue 2010 e)

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

More in Functional Analysis & Transforms

WHAT IS CALCULUS?

FROM SIMPLE ALGEBRA TO DEEP ANALYSIS

Paperback

RRP $68.99

$65.75

Functional Analysis and Operator Algebras : Cms/Caims Books in Mathematics - Kenneth R. Davidson

$116.90

Quaternionic Hilbert Spaces and Slice Hyperholomorphic Functions - Daniel Alpay

$95.90

Introduction to Real Analysis

Hardcover

RRP $219.95

$195.50

11%
OFF

Applied Thematic Analysis

Hardcover

RRP $139.25

$75.35

46%
OFF

Interface Problems for Elliptic Second-Order Equations in Non-Smooth Domains : Frontiers in Mathematics - Mikhail Borsuk

$90.50

25%
OFF

From Frechet Differentials to Firing Tables : The Scope and Sources of Gilbert Ames Bliss' Contributions to World War I Era Ballistics - Alan Gluchoff

RRP $120.00

$101.25

16%
OFF

The Cauchy Transform, Potential Theory and Conformal Mapping

Paperback

RRP $145.00

$108.50

25%
OFF

Integral Transforms and Their Applications

Paperback

RRP $120.00

$90.50

25%
OFF

Preface	p. vii
Fundamentals	p. 1
Topological spaces	p. 1
Normed spaces	p. 8
Dense set and separable space	p. 20
Linear operators	p. 22
Space of bounded linear operators	p. 25
Hahn-Banach theorem and applications	p. 28
Compactness	p. 32
Reflexivity	p. 34
Weak topologies	p. 36
Continuity of mappings	p. 43
Convexity, Smoothness, and Duality Mappings	p. 49
Strict convexity	p. 49
Uniform convexity	p. 53
Modulus of convexity	p. 58
Duality mappings	p. 67
Convex functions	p. 79
Smoothness	p. 91
Modulus of smoothness	p. 94
Uniform smoothness	p. 98
Banach limit	p. 106
Metric projection and retraction mappings	p. 115
Geometric Coefficients of Banach Spaces	p. 127
Asymptotic centers and asymptotic radius	p. 127
The Opial and uniform Opial conditions	p. 136
Normal structure	p. 146
Normal structure coefficient	p. 153
Weak normal structure coefficient	p. 162
Maluta constant	p. 165
GGLD property	p. 172
Existence Theorems in Metric Spaces	p. 175
Contraction mappings and their generalizations	p. 175
Multivalued mappings	p. 188
Convexity structure and fixed points	p. 197
Normal structure coefficient and fixed points	p. 201
Lifschitz's coefficient and fixed points	p. 206
Existence Theorems in Banach Spaces	p. 211
Non-self contraction mappings	p. 211
Nonexpansive mappings	p. 222
Multivalued nonexpansive mappings	p. 237
Asymptotically nonexpansive mappings	p. 243
Uniformly L-Lipschitzian mappings	p. 250
Non-Lipschitzian mappings	p. 259
Pseudocontractive mappings	p. 264
Approximation of Fixed Points	p. 279
Basic properties and lemmas	p. 279
Convergence of successive iterates	p. 286
Mann iteration process	p. 288
Nonexpansive and quasi-nonexpansive mappings	p. 292
The modified Mann iteration process	p. 300
The Ishikawa iteration process	p. 303
The S-iteration process	p. 307
Strong Convergence Theorems	p. 315
Convergence of approximants of self-mappings	p. 315
Convergence of approximants of non-self mappings	p. 324
Convergence of Halpern iteration process	p. 327
Applications of Fixed Point Theorems	p. 333
Attractors of the IFS	p. 333
Best approximation theory	p. 335
Solutions of operator equations	p. 336
Differential and integral equations	p. 339
Variational inequality	p. 341
Variational inclusion problem	p. 343
	p. 349
Basic inequalities	p. 349
Partially ordered set	p. 350
Ultrapowers of Banach spaces	p. 350
Bibliography	p. 353
Index	p. 365
Table of Contents provided by Ingram. All Rights Reserved.

Fixed Point Theory for Lipschitzian-Type Mappings with Applications

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Functional Analysis & Transforms

WHAT IS CALCULUS?

FROM SIMPLE ALGEBRA TO DEEP ANALYSIS

Functional Analysis and Operator Algebras

Cms/Caims Books in Mathematics

Nonlinear Problems of Elasticity

II: 3-Dimensional Bodies

Choquet Integrals and Monotone Sublinear Operators

Frontiers in Mathematics

Convex Functions and Their Applications

A Contemporary Approach

INTRODUCTION TO ANALYSIS WITH COMPLEX NUMBERS

Quaternionic Hilbert Spaces and Slice Hyperholomorphic Functions

Trace Inequalities

For Matrices and Hilbert Space Operators

Mathematical Analysis

Theory and Applications

A Concise Approach to Mathematical Analysis

Introduction to Real Analysis

Applied Thematic Analysis

Interface Problems for Elliptic Second-Order Equations in Non-Smooth Domains

Frontiers in Mathematics

Analysis with Ultrasmall Numbers

Textbooks in Mathematics

From Frechet Differentials to Firing Tables

The Scope and Sources of Gilbert Ames Bliss' Contributions to World War I Era Ballistics

Spectral Theory and Quantum Mechanics

Universitext

Topological Vector Spaces

Chapman & Hall/CRC Pure and Applied Mathematics

Counterexamples

From Elementary Calculus to the Beginnings of Analysis

A Course in Abstract Harmonic Analysis

Textbooks in Mathematics

Number, Shape, & Symmetry

An Introduction to Number Theory, Geometry, and Group Theory

Introduction to Mathematical Proofs

Textbooks in Mathematics

Measure and Integral

An Introduction to Real Analysis, Second Edition

The Cauchy Transform, Potential Theory and Conformal Mapping

Integral Transforms and Their Applications

This product is categorised by

Popular Searches