Research On Some Nonlinear Problems In Menger Probabilistic G-Metric Space

In this paper, we introduce many new concepts in Menger probabilistic G-metric spaces. Based on these new concepts, we study some nonlinear problems in Menger probabilistic G-metric spaces. Meanwhile, as applications of our main results, many examples are given to illustrate the theorems. It is divided into the following three sections. The following chapter:In chapter one, we introduce the development situation, the latest cutting-edge in Menger PGM-spaces. Meantime, we also give some basic concepts in Menger PGM-spaces.In chapter two, we introduce a new concept of common property (E.A) in Menger PGM-spaces and obtain some common fixed point theorems for three pairs of self-mappings satisfying the common property (E.A) in Menger PGM-spaces.In chapter three, we introduce the concepts of generalized probabilistically bounded set and Menger-Hausdorff metric, and we obtain some useful results.Utilizing these concepts and results, we establish some common fixed point theorems for three hybrid pairs of mappings satisfying the common property (E.A)in Menger PGM-spaces.