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	This book has been written as a part of my program of teaching nonlinear functional analysis at the graduate level. Nonlinear functional analysis is an area of mathematics which has suddenly grown up over the past few decades, influenced by nonlinear problems posed in physics, mechanics, operations research and economics. It is no longer a subsidiary of linear functional analysis. Its applicable field is far and away wider than that of the linear case because most of problems arising in natural sciences or social sciences are nonlinear. The main purpose of this book is to present the theory of nonlinear functional analysis in a systematic way with nonlinear operators, fixed point theorems and minimax theorems as essential ingredients and then to give applications of the theory to variational inequalities, games and linear operators.
Professor Wataru Takahashi, Tokyo Institute of Technology, ISBN 4-946552-04-9 Hardcover pp.276 国内価格 6000円+税
ORDER (English)
Contents 1. Preliminaries 1.1 Topological Spaces 1.2 Banach Spaces and Hilbert Spaces 1.3 Lower Semicontinuous and Convex Functions 1.4 Banach Limits and Invariant Means 2. Fixed Point Theory in Metric Spaces 2.1 Existence Theorems in Complete Metric Spaces 2.2 w-Distances on Metric Spaces 2.3 Characterizations of Metric Completeness 3. Fixed Point Theory in Hilbert Spaces 3.1 Some Properties of Hilbert Spaces 3.2 Baillon's Nonlinear Ergodic Theorem 3.3 Fixed Point Theorem for Nonexpansive Semigroups 3.4 Generalized Nonlinear Ergodic Theorems 3.5 Some Nonlinear Ergodic Theorems 3.6 Fixed Point Theorems for Lipschitzian Semigroups 4. Geometry of Banach Spaces 4.1 Convexity of Banach Spaces 4.2 Duality Mappings 4.3 Differentiability of Norms 4.4 Nonexpansive Mappings in Banach Spaces 4.5 Fixed Point Theorems for Nonexpansive Families 4.6 Accretive Operators 5. Convergence Theorems in Banach Spaces 5.1 The Behavior or Resolvents Jr when r -> oo 5.2 The Behaviro or Resolvents Jr when r -> 0 5.3 Nonlinear Ergodic Theorems in Banach Spaces 5.4 The Problem of Image Recovery 5.5 Ergodic Theorems for Linear Operators 6. Fixed Point Theory in Topological Vector Spaces 6.1 Fan-Browder's Fixed Point Theorem 6.2 Ceneralized Fixed Point Theorems 6.3 Minimax Theorems 6.4 Mazur-Orlicz Theorem 6.5 Separation and Best Approximation Theorems 7. Some Applications 7.1 Variational Inequalities 7.2 Cores of Games 7.3 Applications to Linear Operators 7.4 Linear Inequalities and Minimum Norm Problems
Published by Yokohama Publishers