 Discusses topics on basic fixedpoint theorems due Banach, Brouwer, Schauder and Tarski, their variants and their applications
 Introduces finitedimensional degree theory based on Heinz's approach and some geometric coefficients for Banach spaces
 Explains Sharkovsky’s theorem on periodic points and Thron’s results on the convergence of iterates of certain real functions
 Presents two classic counterexamples in fixedpoint theory: one due to Huneke and other due to Kinoshita
 Elaborates Manka’s proof on the fixedpoint property of arcwise connected hereditarily unicoherent continua
 Offers a detailed treatment of Ward’s theory of partially ordered topological spaces culminating in Sherrer theorem
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 About this Textbook

This book provides a primary resource in basic fixedpoint 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 fixedpoint 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 fixedpoint theorem. It elaborates Manka’s proof of the fixedpoint property of arcwise connected hereditarily unicoherent continua, based on the connection he observed between set theory and fixedpoint 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.
 About the authors

P.V. SUBRAHMANYAM is a Professor Emeritus at the Indian Institute of Technology Madras (IIT Madras), India. He received his PhD in Mathematics from IIT Madras, for his dissertation on “Topics in Fixed Point Theory” under the supervision of(late)Dr. V. Subba Rao. He received his MSc degree in Mathematics from IIT Madras, and BSc degree in Mathematics from Madras University. He has held several important administrative positions, such as senior professor and head of the Department of Mathematics at IIT Madras; founder and head of the Department of Mathematics at the Indian Institute of Technology Hyderabad (IIT Hyderabad); Executive Chairman of the Association of Mathematics Teachers of India(AMTI); president of the Forum for Interdisciplinary Mathematics (FIM).Before joinining IIT Madras he served as a faculty member at Loyola College, Madras University, and Hyderabad Central University. His areas of interest include classical analysis, nonlinear analysis and fixedpoint theory, fuzzy set theory, functional equations and mathematics education. He has published over 70 papers and served on the editorial board of the Journal of Analysis and the Journal of Differential Equations and Dynamical Systems. He received an award for his outstanding contributions to mathematical sciences in 2004 and the Lifetime Achievement Award from the FIM in 2016. He has given various invited talks at international conferences and completed brief visiting assignments in many countries such as Canada, Czech Republic, Germany, Greece, Japan, Slovak Republic and the USA. He is also a life member of the Association of Mathematics Teachers of India, FIM, Indian Mathematical Society and the Society for Industrial and Applied Mathematics(SIAM).
 Table of contents (12 chapters)


Prerequisites
Pages 121

Fixed Points of Some Real and Complex Functions
Pages 2350

Fixed Points and Order
Pages 5171

Partially Ordered Topological Spaces and Fixed Points
Pages 7396

Contraction Principle
Pages 97119

Table of contents (12 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Elementary Fixed Point Theorems
 Authors

 P.V. Subrahmanyam
 Series Title
 Forum for Interdisciplinary Mathematics
 Copyright
 2018
 Publisher
 Springer Singapore
 Copyright Holder
 Springer Nature Singapore Pte Ltd.
 eBook ISBN
 9789811331589
 DOI
 10.1007/9789811331589
 Hardcover ISBN
 9789811331572
 Series ISSN
 23646748
 Edition Number
 1
 Number of Pages
 XIII, 302
 Number of Illustrations
 5 b/w illustrations
 Topics