This book contains selected chapters discussing both theoretical foundations and practical applications of fixed-point theory. It focuses on fundamental theorems on the existence and uniqueness of mappings arranged in a progressive manner. This book covers applications related to topological properties, the existence, and uniqueness of solutions for different classes of integral equations, nonlinear and fractional differential equations, dynamic programming problems, and challenges in engineering sciences. With 17 chapters contributed by global researchers on fixed-point theory, a distinguishing feature of this book is its visual representation of examples illustrating key results, making complex concepts more accessible and easier to grasp.

This book is an essential resource for researchers, academicians, and graduate students in the fields of pure and applied mathematics. Additionally, due to its strong emphasis on practical problem-solving, it serves as a highly valuable reference for engineers, computational scientists, and industry professionals dealing with nonlinear modeling, dynamic programming, and mathematical engineering challenges.

Mahpeyker Öztürk is a full professor in the Department of Mathematics at Sakarya University, Turkey. Her research expertise encompasses functional analysis, fixed-point theory, topology and nonlinear analysis. After earning her Ph.D. from Sakarya University in 2011, she built a highly productive academic career at the same institution, serving in various teaching, research, and administrative capacities. Professor Öztürk has published extensively in leading international journals and is deeply committed to mentoring young mathematicians through her supervision of graduate research. She serves on editorial boards of several scholarly journals and has been involved in organizing and participating in numerous international conferences and workshops. Her substantial contributions to mathematics reflect her deep dedication to the advancement of the field.

Mudasir Younis is an assistant professor in the Department of Mathematics at Sakarya University, Turkey. Earlier, he was a postdoct fellow in the Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Uttar Pradesh, India. He has focused his research on developing fixed-point theory within the framework of graph-structured metric spaces, a burgeoning area in mathematical analysis. His contributions have led to several breakthrough results, deepening the theoretical foundations of fixed-point theorems and expanding their applications. He has also tackled the existence of solutions to a range of real-world problems in engineering, physics, and applied sciences, including models such as damped spring-mass systems, elastic beam deformations, vibrations of heavy hanging cables, rocket ascent dynamics, and electrical tuning circuits. With a prolific research portfolio exceeding 45 publications in reputable journals, he has garnered national and international acclaim, including prestigious fellowships such as the Abel Visiting Scholar Program (2022).

Erdal Karapınar is a full professor in the Department of Mathematics at Atılım University, Turkey. A renowned mathematician, his expertise spans functional analysis, operator theory, linear topological invariants, fixed-point theory, and best approximation theory. He earned his Ph.D. in 2004 from the Middle East Technical University in Ankara, Turkey, with a dissertation titled “Isomorphisms of ℓ-Köthe spaces,” under the mentorship of Prof. Vyacheslav Pavlovich Zakharyuta and Prof. Murat Yurdakul. His academic journey includes research and teaching positions at China Medical University in Taiwan and İzmir University of Economics in Turkey. He has authored numerous articles in prestigious international journals, published four scholarly books with Springer, and contributed several chapters to other academic volumes. His impactful scholarship earned him recognition as a Highly Cited Researcher by Clarivate Analytics for five consecutive years (2015–2019).