LAUSR

In this paper, existence and uniqueness of a fixed point for non-self mappings with nonlinear contractive condition in the sense of Fang [On φ-contractions in probabilistic and fuzzy metric spaces. Fuzzy Set Syst. (267) 2015, 86–99] will be proved, using the notion of strictly convex structure introduced by Ješić et al. [Ješić, S.N, Nikolić, R.M., Babačev N.A., A Common Fixed Point Theorem in Strictly Convex Menger PM-spaces, Filomat (28)(4) 2014, 735–743] for Menger PM-spaces. As a consequence of main result we will give probabilistic generalization of Assad and Kirk’s result [Assad, N.A., Kirk, W.A., Fixed-point theorems for set-valued mappings of contractive type. Pacific J. Math. (43) 1972, 553–562].