Nonlinear Elastic Matching Distances and Fixed Point Theory

Nonlinear Elastic Matching Distances and Fixed Point Theory

von Hemen Dutta

This book offers an in-depth exploration of fixed point theory within a mathematical framework known as nonlinear elastic matching distance spaces. Specifically, the authors discuss new mathematical tools to handle complex systems where several elements interact at once and influence each other in complex ways. Traditional methods are usually able to measure relationships between two things at a time, but many real-world problems in areas such as engineering, data science, economics, and computer modeling involve multiple interactions and nonlinear changes that traditional/classical approaches cannot capture fully. By developing a broader and more flexible framework, the authors provide improved methods to study stability, recurring processes, and long-term behavior in complex systems to meet the growing demand for stronger mathematical foundations in modern research and technology. Building from fundamentals including topology, convergence, and completeness, the book reinterprets classical results such as Banach’s contraction principle in this broader setting. The authors then move on to advanced topics including weak and generalized contractions, ordered structures, cyclic and non-self mappings, best proximity points, and multi-variable fixed point results, along with the stability of iterative processes. With carefully worked examples, applications to nonlinear integral and functional equations, and exercises throughout, the book serves as a valuable research guide and as a graduate-level reference book for those looking to engage deeply with modern developments in nonlinear analysis.

This book offers an in-depth exploration of fixed point theory within a mathematical framework known as nonlinear elastic matching distance spaces. Specifically, the authors discuss new mathematical tools to handle complex systems where several elements interact at once and influence each other in complex ways. Traditional methods are usually able to measure relationships between two things at a time, but many real-world problems in areas such as engineering, data science, economics, and computer modeling involve multiple interactions and nonlinear changes that traditional/classical approaches cannot capture fully. By developing a broader and more flexible framework, the authors provide improved methods to study stability, recurring processes, and long-term behavior in complex systems to meet the growing demand for stronger mathematical foundations in modern research and technology. Building from fundamentals including topology, convergence, and completeness, the book reinterprets classical results such as Banach’s contraction principle in this broader setting. The authors then move on to advanced topics including weak and generalized contractions, ordered structures, cyclic and non-self mappings, best proximity points, and multi-variable fixed point results, along with the stability of iterative processes. With carefully worked examples, applications to nonlinear integral and functional equations, and exercises throughout, the book serves as a valuable research guide and as a graduate-level reference book for those looking to engage deeply with modern developments in nonlinear analysis.

In addition, this book:

• Presents new, practical tools for studying stability, designing iterative methods, and analyzing nonlinear models
• Discusses weak and generalized contractions, cyclic mappings, and multi-variable fixed point results
• Supports independent thinking and the ability to contribute to current developments in nonlinear analysis

Highlights

• Presents new, practical tools for studying stability, designing iterative methods, and analyzing nonlinear models Discusses weak and generalized contractions, cyclic mappings, and multi-variable fixed point results Supports independent thinking and the ability to contribute to current developments in nonlinear analysis

Über den Autor

Hemen Dutta, Ph.D., is a Professor in the Department of Mathematics at Gauhati University, Guwahati, India. He has published over 200 publications as research articles, proceedings papers, and book chapters and has also authored and edited several books published by leading publishers. He has organized many academic events and served as a speaker in various national and international events. He is on the editorial board of several SCI/SCIE and Scopus indexed journals and is the receipt of several research projects and grants from various funding agencies. His research interests include applied analysis and mathematical modeling.

Nisha Sharma is a Lecturer in the Department of Mathematics at Pt. J.L.N. Govt. College, Faridabad, India. Her research interests include fixed point theory, approximation theory, and positive linear operators, specifically the structural development of generalized distance spaces, operator-based approximation methods, and the study of convergence through moment techniques and iterative schemes. She has published several research papers and book chapters in reputed journals and edited books.