This book offers a comprehensive exploration of the Banach contraction principle and its many facets. A compilation of chapters authored by global experts, it is aimed at researchers and graduate students in mathematics. The content covers the Banach contraction principle, its generalizations, extensions, consequences and applications, focusing on both single-valued and multi-valued mappings across various spaces. While discussing theoretical foundations, this book uniquely emphasizes the practical applications of the Banach contraction principle in real-world problem-solving scenarios.

Each chapter addresses specific topics, including fractals, fractional differentials, integral equations, elastic beam problems and mathematical modeling and analysis of electrical circuits. These diverse subjects showcase the principle's versatility in solving complex issues that go beyond theoretical mathematics. By highlighting Banach's contraction principle as a lasting legacy, the book not only honours past mathematical achievements but also anticipates future innovations in industrial and applied mathematics. It underscores the enduring relevance of the principle, ensuring its continued prominence in mathematical discourse and its pivotal role in driving advancements across the field. This comprehensive exploration catalyzes inspiring future developments in mathematical research.

Offers a comprehensive exploration of the Banach contraction principle, spanning a century of development Delves into extensions, generalizations, and cutting-edge applications of the Banach contraction principle Discusses applications in probability theory, statistics, numerical analysis, physics, systems, and control theory

Autorentext

Anita Tomar is Professor and Head of the Department of Mathematics at Pt. L.M.S. Campus of Sri Dev Suman Uttarakhand University, Rishikesh, Uttrakhand, India. Specializing in fixed-point theory, she has authored/coauthored 95 research publications, 10 textbooks, 10 book chapters and an edited book titled Fixed Point Theory and its Applications to Real World Problems. She has delivered talks internationally and supervised two research scholars. She has served as a guest editor for special issues in the Journal of Function Spaces, Demonstratio Mathematica and the Journal of Mathematical Sciences. She is a reviewer for Mathematical Reviews (AMS) and has reviewed numerous papers indexed in MathSciNet, ZbMATH and Scopus.

A life member of the Indian Mathematical Society and Indian Society for History of Mathematics, she has received several awards and recognition, such as the Teacher of the Year (2020), Leading Women Scientist (2021), the Chief Minister Excellence and Good Governance Award (2022) and the Excellence in Research (2023) award. In addition to research, she has contributed to syllabus development under the NEP 2020 for Uttarakhand universities and actively participates in both academic and administrative roles in the university. She is deeply dedicated to advancing mathematics through innovative research, fostering interdisciplinary collaboration and promoting excellence in education.

Manish Jain is Assistant Professor in the Department of Mathematics at Ahir College, Rewari, Haryana, India. He is Fellow of the Institute of Mathematics and Its Applications (FIMA), UK, and has been recognized as a Friend of OWSD, an international organization under UNESCO. An accomplished researcher in pure and applied mathematics, he specializes in real analysis, functional analysis and fixed-point theory. He has served as a reviewer for several publications and has delivered talks at various conferences. With over 31 publications in leading journals, he is deeply dedicated to advancing mathematics through research, interdisciplinary collaboration and education.

Inhalt

Common fixed point for pairs of Weakly compatible mappings using F-contraction.- Coincidence points of mappings on relational metric Spaces with applications.- Some fixed point result in m-metric space using different contractions.- Application of common fixed point in the framework of b-metric space via simulation function.- Relation-theoretic fixed point results in extended Rectangular mr-metric spaces.- Julia fractals of complex-valued cosine functions via fixed point iterations.- Some fixed-circle results with mix-type contractions on metric spaces.- Application of fixed point iterations in generation of fractals for higher-order complex polynomial.- Rational type fixed-disc and common fixed-disc results on metric and s-metric spaces via Geraghty type contractions.- Coupled Fixed Points in Ordered Fuzzy Metric Spaces and an Elastic Beam Problem.- Data Dependence, Stability and Convergence Rate of Novel Iterative Algorithm.- A New Generalization of Metric Space and Banach Contraction Principle.- Trajectory and Exact Controllability results on Impulsive Nonlocal Differential System with Deviated Argument.- Banach contraction in Altering JS-metric space to decipher aggregate voltage of electric circuit.- Common fixed point for families of weakly subsequentially continuous mappings.