A Study of Some Fixed Point Theorems in Probabilistic Metric Spaces

In this research, we continue to study some common fixed point theorems in the setting of probabilistic metric spaces under various generalized contraction conditions. At the beginning of our research we study some basic definitions and results used throughout the research work. We begin our results by giving a comment on some known result of Sharma and Deshpande and we give an example to justify our claim. Also, we prove a common fixed point theorem for two pairs of weakly compatible mappings in Menger spaces without appeal to continuity condition. We obtain a common fixed point theorem for three pairs of weakly compatible mappings in Menger spaces with applying the common property (E. A). Then, common fixed point theorems for family of occasionally weakly compatible self mappings in Menger and D-Menger spaces are obtained. Furthermore, some new fixed point theorems in 2-Menger spaces considering two distribution functions and using new contraction conditions are obtained. Moreover, we prove a fixed point theorem for non-self mappings in two 2-Menger spaces. Finally, we prove a common fixed point theorem for six compatible self mappings of type (A) in a complete non-Archimedean Menger space