Introduction to Nonlinear Analysis and Fixed Point Theory

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.

“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)

• ​Chapter 1. Fundamentals.- Chapter 2. Geometry in Banach Spaces and Duality Mappings.- Chapter 3. Differential Calculus in Banach Spaces.- Chapter 4. Monotone Operators, Phi-accretive Operators and Their Generalizations.- Chapter 5. Fixed Point Theorems.- Chapter 6. Degree Theory, K-Set 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.