Genericity in Nonlinear Analysis

Preface.- 1. Introduction.- 2. Fixed Point Results and Convergence of Powers of Operators.- 3. Contractive Mappings.- 4. Dynamical Systems with Convex Lyapunov Functions.- 5. Relatively Nonexpansive Operators with Respect to Bregman Distances.- 6. Infinite Products.- 7. Best Approximation.- 8. Descent Methods.- 9. Set-Valued Mappings.- 10. Minimal Configurations in the Aubry-Mather Theory.- References.- Index.

Simeon Reich is the Lord Leonard Wolfson Academic Chair and Professor of Mathematics at Technion-Israel Institute of Technology in Haifa. He has published more than fifty articles in mathematics journals including the Journal of Nonlinear Convex Analysis, SIAM Journal of Optimization, and Journal of Applied Analysis and fifteen books.

Alexander J. Zaslavski is a Senior Researcher in the Department of Mathematics at Technion-Israel Institute of Technology in Haifa. He has published over one hundred journal articles, and has authored books including Optimization on Metric and Normed Spaces (Springer, 2010) and Nonconvex Optimal Control and Variational Problems (Springer, 2013).

From the book reviews:

"This book contains an extensive collection of current results with solid proofs and each chapter is self-contained. It can be used as a supplementary material for graduate courses in nonlinear functional analysis, optimization theory and approximation theory. It is also a rich source of problems and results for researchers and practitioners working in mathematics and the mathematical sciences." (Sehie Park, Mathematical Reviews, August, 2014)

"The book, which is self-contained and very well-written, is the first book to present an extensive collection of generic results in nonlinear analysis. As such, this book should prove useful to those currently doing research in nonlinear analysis and to those interested in beginning research in nonlinear analysis." (Barry Turett, zbMATH, Vol. 1296, 2014)

"The book ... contains a lot of interesting and deep generic existence results for some classes of problems in nonlinear analysis. By bringing together results spread through various journals, it will be of great help for researchers in fixed point theory, optimization, best approximation and dynamical systems. Being carefully written, with complete proofs and illuminating examples, it can serve also as an introductory book to this areas of current research." (S. Cobzas, Studia Universitatis Babes-Bolyai, Mathematica, Vol. 59 (1), 2014)