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An Introduction to Nonlinear Analysis and Fixed Point Theory

  • Textbook
  • © 2018

Overview

Authors:
  1. Hemant Kumar Pathak

    1. School of Studies in Mathematics, Pandit Ravishankar Shukla University, Raipur, India

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

  • Discusses applications in 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

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xxvii
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  2. Fundamentals

    • Hemant Kumar Pathak
    Pages 1-101

  3. Geometry of Banach Spaces and Duality Mapping

    • Hemant Kumar Pathak
    Pages 103-127

  4. Differential Calculus in Banach Spaces

    • Hemant Kumar Pathak
    Pages 129-176

  5. Monotone Operators, Strongly \(\phi \)-Accretive Operators and Their Variants

    • Hemant Kumar Pathak
    Pages 177-230

  6. Fixed Point Theorems

    • Hemant Kumar Pathak
    Pages 231-448

  7. Degree Theory, k-Set Contractions and Condensing Operators

    • Hemant Kumar Pathak
    Pages 449-511

  8. Variational Methods and Optimization

    • Hemant Kumar Pathak
    Pages 513-606

  9. Applications of Monotone Operator Theory

    • Hemant Kumar Pathak
    Pages 607-658

  10. Applications of Fixed Point Theorems

    • Hemant Kumar Pathak
    Pages 659-763

  11. Applications of Fixed Point Theorems for Multifunction to Integral Inclusions

    • Hemant Kumar Pathak
    Pages 765-791

  12. Back Matter

    Pages 793-830
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Keywords

About this book

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.


Reviews

“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)

Authors and Affiliations

  • School of Studies in Mathematics, Pandit Ravishankar Shukla University, Raipur, India

    Hemant Kumar Pathak

About the author

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.

Bibliographic Information

  • Book Title: An Introduction to Nonlinear Analysis and Fixed Point Theory

  • Authors: Hemant Kumar Pathak

  • DOI: https://doi.org/10.1007/978-981-10-8866-7

  • Publisher: Springer Singapore

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Singapore Pte Ltd. 2018

  • Hardcover ISBN: 978-981-10-8865-0Published: 31 May 2018

  • Softcover ISBN: 978-981-13-4261-5Published: 23 December 2018

  • eBook ISBN: 978-981-10-8866-7Published: 19 May 2018

  • Edition Number: 1

  • Number of Pages: XXVII, 830

  • Number of Illustrations: 29 b/w illustrations

  • Topics: Analysis

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