Razieh Farokhzad Rostami
Abstract
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. ...
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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.
