Fixed point theorems for non-self mappings with nonlinear contractive condition in strictly convex Menger PM-spaces

In this paper, existence and uniqueness of a fixed point for non-self mappings with nonlinear contractive condition in the sense of Fang [On co-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 Jesic et al. [Jesic, S.N, Nikolic, R.M., Babaeev 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].