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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.
Professor Simeon Reich was born in Krakow, Poland, in 1948. He is a Professor Emeritus of Mathematics at the Technion – Israel Institute of Technology, Haifa, Israel, where he received his BSc (1970) and DSc (1973) degrees. He taught previously at Tel Aviv University, the University of Chicago, the University of Southern California, the University of California at Berkeley, the University of California at Santa Barbara, the Tokyo Institute of Technology, and at UMCS (Lublin). Professor Reich's areas of research include nonlinear operator theory, nonlinear evolution and integral equations, the identification and estimation of nonlinear distributed parameter systems, infinite dimensional holomorphy, variational inequalities, and sequential and parallel algorithms in feasibility and optimization. His list of publications contains four monographs, twenty-one edited volumes and more than 600 research papers on Nonlinear Analysis and Optimization. Professor Reich has supervised seventeen PhD students and ten MSc students.
Doctor Alexander J. Zaslavski was born in Kirovograd, Ukraine in 1957. He is a senior researcher at the Technion - Israel Institute of Technology. His areas of research include nonlinear operator theory, optimization, the calculus of variations, optimal control, game theory, dynamical system theory and mathematical economics. Alexander Zaslavski is the author of 28 research monographs and more than 600 research papers.