عنوان

Elementary fixed point theorems /

(Number (ISBN

9789811331589

(Number (ISBN

9811331588

Erroneous ISBN

9789811331572

Erroneous ISBN

981133157X

Title Proper

Elementary fixed point theorems /

General Material Designation

[Book]

First Statement of Responsibility

P.V. Subrahmanyam.

Place of Publication, Distribution, etc.

Singapore :

Name of Publisher, Distributor, etc.

Springer,

Date of Publication, Distribution, etc.

2018.

Specific Material Designation and Extent of Item

1 online resource (xiii, 302 pages) :

Other Physical Details

illustrations

Series Title

Forum for Interdisciplinary Mathematics,

ISSN of Series

2364-6748

Text of Note

Includes bibliographical references.

Text of Note

Chapter 1. Prerequisites -- Chapter 2. Fixed Points of Some Real and Complex Functions -- Chapter 3. Fixed Points and Order -- Chapter 4. Partially Ordered Topological Spaces and Fixed Points -- Chapter 5. Contraction Principle -- Chapter 6. Applications of the Contraction Principle -- Chapter 7. Caristi's fixed point theorem -- Chapter 8. Contractive and Nonexpansive Mappings -- Chapter 9. Geometric Aspects of Banach Spaces and Nonexpansive Mappings -- Chapter 10. Brouwer's Fixed Point Theorem -- Chapter 11. Schauder's Fixed Point Theorem and Allied Theorems -- Chapter 12. Basic Analytic Degree Theory af a Mapping.

0

Text of Note

This book provides a primary resource in basic fixed-point theorems due to Banach, Brouwer, Schauder and Tarski and their applications. Key topics covered include Sharkovsky's theorem on periodic points, Thron's results on the convergence of certain real iterates, Shield's common fixed theorem for a commuting family of analytic functions and Bergweiler's existence theorem on fixed points of the composition of certain meromorphic functions with transcendental entire functions. Generalizations of Tarski's theorem by Merrifield and Stein and Abian's proof of the equivalence of Bourbaki-Zermelo fixed-point theorem and the Axiom of Choice are described in the setting of posets. A detailed treatment of Ward's theory of partially ordered topological spaces culminates in Sherrer fixed-point theorem. It elaborates Manka's proof of the fixed-point property of arcwise connected hereditarily unicoherent continua, based on the connection he observed between set theory and fixed-point theory via a certain partial order. Contraction principle is provided with two proofs: one due to Palais and the other due to Barranga. Applications of the contraction principle include the proofs of algebraic Weierstrass preparation theorem, a Cauchy-Kowalevsky theorem for partial differential equations and the central limit theorem. It also provides a proof of the converse of the contraction principle due to Jachymski, a proof of fixed point theorem for continuous generalized contractions, a proof of Browder-Gohde-Kirk fixed point theorem, a proof of Stalling's generalization of Brouwer's theorem, examine Caristi's fixed point theorem, and highlights Kakutani's theorems on common fixed points and their applications.--

Source for Acquisition/Subscription Address

Springer Nature

Stock Number

com.springer.onix.9789811331589

International Standard Book Number

9789811331572

International Standard Book Number

9789811331596

Fixed point theory.

Fixed point theory.

MAT034000

PBK

PBK

Number

Edition

Class number

Subrahmanyam, P. V.

Date of Transaction

20200823234703.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y