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.
Hemant Kumar Pathak is professor and head of the School of Studies in Mathematics at Pt. Ravishankar Shukla University, Raipur, India. He is also the dean of science, member of the standing committee, director of the Center for Basic Sciences (CBS) and director of Human Resource Development Centre at Pt. Ravishankar Shukla University. He also has worked at Kalyan Mahavidyalaya, Bhilai Nagar, and the Government Postgraduate College, Dhamtari, India. He earned his PhD from Pt. Ravishankar Shukla University in 1988. Professor Pathak has been awarded the “Distinguished Service Award 2011” by the Vijnana Parishad of India. With teaching and research experience of over 39 years, he has published more than 233 research papers in leading international journals in areas of approximation theory, operator theory, integration theory, fixed point theory, number theory, cryptography, summability theory and fuzzy set theory.
Professor Pathak is on the editorial board of the American Journal of Computational and Applied Mathematics, Fixed Point Theory and Applications (Springer), Journal of Modern Methods in Numerical Mathematics, and the guest editor of the Indian Journal of Mathematics (2012-2013). He also is reviewer of the Mathematical Review of the American Mathematical Society. A member of several national and international scientific societies: American Mathematical Society, U.S.A. (1991–1995), International Federation of Nonlinear Analysts, U.S.A. (1996–2008), and Indian Science Congress Association (1985–1986), Professor Pathak is life member of the Allahabad Mathematical Society, Bharata Ganita Parishad, The Vijnana Parishad of India, Calcutta Mathematical Society and National Academy of Mathematics.
