This contributed volume contains chapters on various fixed-point theorems, including those in metric, b-metric and partial metric spaces. The book addresses the need for rigorous analytical methods in optimization, computational mathematics and applied sciences. By offering innovative solutions through iterative schemes and contraction principles, it bridges the gap between abstract mathematical principles and practical problem-solving approaches. The concept of fixed points has deep mathematical significance, influencing both theoretical frameworks and real-world applications. The book highlights the applications of fixed-point theory, presenting fundamental concepts and modern advancements, in diverse fields such as traffic control systems, stock market analysis, iterative algorithms and differential equations.

Autorentext

Anita Tomar is the Professor and Head of the Department of Mathematics at Pt. L.M.S. Campus, Sri Dev Suman Uttarakhand University, Rishikesh. Her research interests encompass real and complex dynamics, with a focus on chaos, fractals, mathematical modeling, and fixed-point theory. She has contributed significantly to these fields, authoring 105 research papers and 15 book chapters, and edited books titled "Fixed Point Theory & its Applications to Real World Problems", Adhunik Pridrishya Me Bharatiya Prachiya Gyaan Sampada (Connecting Ancient Indian Wisdom in Modern Contexts)(Set of 2 Vol), and "Banach Contraction Principle: A Centurial Journey" . Additionally, Prof. Tomar has been actively involved in applied mathematics and the history of mathematics. She has delivered talks in various countries, including Senegal, Turkey, Nepal, Taiwan, and Thailand, as well as across India. She has supervised 2 research scholars, co-authored textbooks, and served as a guest editor for special issues in journals such as the Journal of Function Spaces, Journal of Mathematical Sciences and Demonstratio Mathematica.

Prof. Tomar is also a reviewer for Mathematical Reviews (AMS) and has reviewed numerous papers indexed in MathSciNet, ZbMATH, and Scopus. Her accolades include the "Teacher of the Year" award in 2020, the "Leading Women Scientist" award in 2021, and the "Chief Minister's Excellence and Good Governance Award" in 2022, "Excellence in Research award" in 2023, Distinguished Service Award in 2025, Best Project Award 2025.

Beyond her research, Prof. Tomar has contributed to syllabus development under NEP 2020 for universities in Uttarakhand and actively participates in both academic and administrative roles. She serves on several key university bodies, including the Director, Centre of Excellence in Entrepreneurship and Incubation, Director, Faculty Development Centre, Executive Council, Academic Council, Board of Studies, Research Degree Committee (RDC), and Interview Boards. She holds life memberships in the Indian Mathematical Society and the Indian Society for History of Mathematics, Vijñana Parishad of India.

She is deeply committed to advancing mathematics through innovative research, fostering interdisciplinary collaboration, and promoting excellence in education.

Manish Jain, FIMA (UK) and recognized as a Friend of OWSD (UNESCO), is Assistant Professor in the Department of Mathematics at Ahir College, Rewari, Haryana, India. He is a distinguished mathematician whose scholarly expertise in real analysis, functional analysis and fixed point theory, with far-reaching implications for both pure and applied mathematics. His research is characterized by conceptual depth and practical relevance, bridging abstract theory with contemporary scientific challenges. He has contributed to the global mathematical community in editorial capacities for several leading international journals, including the TWMS Journal of Applied and Engineering Mathematics. His academic influence extends beyond publications, marked by invited keynote addresses at prestigious international forums in China and active participation in major academic events across Turkey, South Africa, Argentina and India.

With more than 30 research publications in reputed international journals, he continues to advance the frontiers of mathematical sciences through innovative inquiry, interdisciplinary collaboration and a sustained commitment to pedagogical excellence. His recent editorial endeavor in Banach Contraction Principle: A Centurial Journey reflects his deep engagement with foundational mathematical principles and their evolving applications in modern science. A recipient of the Best Researcher Award (National Faculty Award 2023-24), he holds lifetime membership of the Indian Mathematical Society and is a member of the International Society for Fuzzy Set Extensions and Applications. He has also played an instrumental role in strengthening the academic ecosystem by serving on the organizing committees of numerous national and international conferences.