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.
