Fixed Point Results under (ϕ, ψ)-Contractive Conditions and their Application in Optimization Problems

Fixed point theorems can be used to prove the solvability of optimization problems‎, ‎differential equations and equilibrium problems, and‎ ‎the intrinsic flexibility of probabilistic metric spaces makes it possible to extend the idea of contraction mapping in several inequivalent ways‎. ‎In this paper‎, ‎we extend very recent fixed point theorems in the setting of Menger probabilistic metric spaces‎. ‎We present some fixed point theorems for self-mappings satisfying a generalized (ϕ , ψ ) - contractive condition in Menger probabilistic metric spaces which are contractions used extensively in global optimization problems‎. ‎On the other hand‎, ‎we consider a more general class of auxiliary functions in the contractivity condition and prove the existence of fixed points of non-expansive mappings on Menger probabilistic metric spaces.