Nonlinear Elastic Matching Distances and Fixed Point Theory

Erscheinungsjahr 2026
ISBN: 978-3-032-29191-2
Verlag: Springer

Buch, Englisch, 251 Seiten, Format (B × H): 168 mm x 240 mm

Reihe: Synthesis Lectures on Mathematics & Statistics

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.

Zielgruppe

Professional/practitioner

Autoren/Hrsg.

Dutta, Hemen

Sharma, Nisha

Fachgebiete

• Mathematik | Informatik Mathematik Topologie
• Mathematik | Informatik Mathematik Mathematik Allgemein
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis

Inhaltsverzeichnis

Prerequisites of Nonlinear Elastic Matching Distance Spaces.- Preordered Fixed Points in Nonlinear Elastic Matching Distance Spaces.- Elastic Contractive Mappings and Fixed Points.- Property P and Stability of Iterative Processes.- Coupled and Coincidence Fixed Points.- Multidimensional and n-tuple Fixed Point Theory.- Asymptotic Geometry and Iterative Dynamics of Elastic Matching Spaces.

Über Autor(innen)

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.