An Introduction to Nonlinear Analysis and Fixed Point Theory

Beschreibung

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 deep-rooted 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.

Introduces all major topics in nonlinear analysis and fixed point theory in a systematics way

Discusses applications to a wide range of fields ranging from engineering to space science, hydromechanics to astrophysics, chemistry to biology, theoretical mechanics to biomechanics and economics to stochastic game theory

Is useful to graduate and senior undergraduate students of mathematics and engineering

Autor*in

Hemant Kumar Pathak

Themen in »An Introduction to Nonlinear Analysis and Fixed Point Theory«

Topological Spaces Sobolev spaces Banach Spaces Duality mapping Monotone Operators Phi-accretive Operators Fixed Point Theorems Degree Theory Measure of noncompactness Condensing operators Nonlinear integral inclusions

Stimmen zu »An Introduction to Nonlinear Analysis and Fixed Point Theory«

“This book cover many important fundamental concepts and various techniques. It shall be very useful for both students and researchers to understand and to prepare themselves for conducting research in these two areas.” (Satit Saejung, zbMATH 1447.47002, 2020)

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