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 Description
 xxvii, 830 pages : illustrations ; 24 cm
 Notes
 Contents: Chapter 1. Fundamentals  Chapter 2. Geometry in Banach Spaces and Duality Mappings  Chapter 3. Differential Calculus in Banach Spaces  Chapter 4. Monotone Operators, Phiaccretive Operators and Their Generalizations  Chapter 5. Fixed Point Theorems  Chapter 6. Degree Theory, KSet Contractions and Condensing Operators  Chapter 7. Random Fixed Point Theory and Monotone Operators  Chapter 8. Applications of Monotone Operator Theory to Differential and Integral Equations  Chapter 9. Applications of Fixed Point Theorems  Chapter 10. Applications of Fixed Point Theorems for Multifunction to Integral Inclusions.Includes bibliographical references and index.Summary: This book systematically introduces the theory of nonlinear analysis, providing an overview of topics such as geometry of Banach spaces, differential calculus in Banach spaces, monotone operators, and fixed point theorems. It also discusses degree theory, nonlinear matrix equations, control theory, differential and integral equations, and inclusions. The book presents surjectivity theorems, variational inequalities, stochastic game theory and mathematical biology, along with a large number of applications of these theories in various other disciplines. Nonlinear analysis is characterised by its applications in numerous interdisciplinary fields, ranging from engineering to space science, hydromechanics to astrophysics, chemistry to biology, theoretical mechanics to biomechanics and economics to stochastic game theory. Organised into ten chapters, the book shows the elegance of the subject and its deeprooted concepts and techniques, which provide the tools for developing more realistic and accurate models for a variety of phenomena encountered in diverse applied fields. It is intended for graduate and undergraduate students of mathematics and engineering who are familiar with discrete mathematical structures, differential and integral equations, operator theory, measure theory, Banach and Hilbert spaces, locally convex topological vector spaces, and linear functional analysis.