Common Fixed Point Theorems for Harmonic Mapping Pairs in Probabilistic Metric Spaces

In this paper, we introduce the harmonic concepts of set-valued mappings and single-valued mappings in non-Archimedes Menger probabilistic metric spaces. By using the concepts of harmonic mapping pairs in probabilistic metric spaces, we studied the existence of common fixed points for a class of integral type harmonic mappings. And the common fixed point theorems for this kind of harmonic mapping pairs were established, and the random fixed points of these integral type harmonic mappings were further discussed. Therefore, some known results are improved and generalized.