The theory of nonlinear Lipschitz operators and Application

This book is based on the theory of nonlinear (Lipschitz) operators. Recently, Lipschitz versions of different types of linear operators were investigated in several papers, as summability, ideals, convexity, and compacteness of Lipschits operators. There are not many books exclusively dealing with the propertie of nonlinear operators as: summability and ideals theory of nonlinear operators.In this book we present the theory of summability of Lipschitz operators, also some properties of linear operators which generalized to Lipschitz operatorsn their excellent book Framer and Johnson have introduce the theory of summability Lipschitz operators between pointed metric spaces and showed that it is a good generalization of the concept of linear p-summing operators between Banach spaces. This work marked the beginning of the theory of generalization of properties of linear operators to nonlinear case. Even in this much simpler case it becomes clear that we cannot hope to get n complete description of all properties of linear operators which generalized to Lipschitz operators. Therefore, we must limit ourselves to particular the dirent notions of Lipschitz operators which exists.