The book aims to present both well-established and new findings regarding fixed points of nonlinear operators and the convergence of their infinite products. It discusses a range of topics, including various classes of operators, set-valued mappings, genericity, and porosity results in nonlinear analysis, as well as monotone nonexpansive mappings, uniformly locally nonexpansive mappings, operators on metric spaces with graphs, and dynamical systems with convex Lyapunov functions.
The book investigates the existence of fixed points for nonlinear operators and the convergence of their iterates to these fixed points. It addresses self-mappings within complete metric spaces, as well as operators that map a subset of the space back into the space itself. Many of the results presented focus on the iterates of operators in the presence of computational errors, making them applicable in fields such as numerical analysis and computer science.
This book is a valuable resource for researchers in nonlinear analysis and fixed-point theory, and it serves as a foundation for graduate-level courses.
