In collaboration with Payame Noor University and the Iranian Society of Instrumentation and Control Engineers

Document Type : Research Article

Author

Department of Mathematics and statistics‎, ‎Gonbad Kavous University of Gonbad Kavous‎, ‎P.O‎. ‎Box‎. ‎49717-99151‎, ‎Golestan‎, ‎Iran‎.

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. ‎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.

Keywords

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