Elementary Fixed Point Theorems

Discusses topics on basic fixed-point theorems due to Banach, Brouwer, Schauder and Tarski, their variants and their applications

Introduces finite-dimensional 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 counter-examples in fixed-point theory: one due to Huneke and other due to Kinoshita

Elaborates Manka's proof on the fixed-point property of arcwise connected hereditarily unicoherent continua

Offers a detailed treatment of Ward's theory of partially ordered topological spaces culminating in Sherrer theorem

Auteur
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 fixed-point 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).

Contenu

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 xed 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.