Probabilistic Extension of a General Fixed Point Theorem

Abstract

As a probabilistic extension of the theorem obtained by Pant et. al [R.P. Pant, V. Rakoˇcevi´c, D. Gopal, A. Pant, M. Ram, A General Fixed Point Theorem, Filomat 35(12) (2021), 4061–4072], in this paper we prove existence and uniqueness of a fixed point for a wide class of self-mapping defined on complete Menger PM-space. Our theorem generalize well-known fixed point theorems proved for Menger PM-spaces. Also, this theorem characterizes probabilistic metric completeness. Some examples and comments
are given according to the obtained results.