Research On Some Problems Of Fixed Point For Nonlinear Mappings In Probabilistic Metric Spaces

In this paper, we introduced many new concepts in Menger PGM- spaces and Menger PM-spaces, then we obtained many new results about fixed point by introduced new contraction conditions. Some corresponding theorems and common fixed point theorems was introduced and processed in this paper. It is divided into the following three sections:In chapter one, we introduced the development, the latest cutting-edge and the related issues of the research in Menger PGM- spaces and Menger PM-spaces of nonlinear functional analysis. Meantime, we also give out some basic definitions and theorems in Menger probabilistic metric spaces.In chapter two, we research on some common fixed point theorems for compatible and weakly compatible mappings in Menger PGM-metric spaces, obtain many results. After that, we give out an application.In chapter three, we research the existence and uniqueness on some new multipled common fixed point theorems in Menger PM-spaces, obtain many new results. The last, combing the new multiped common fixed point theorem, we give out an application.