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A probabilistic version of the Meir-Keeler type fixed point theorem, which characterizes completeness of themetric space is established. In addition to it, a fixed point theorem for non-expansive mappings satisfying(−δ)type condition in Menger probabilistic metric space (Menger PM-space) is proved. As a byproduct we find anaffirmative answer to the open question on the existence of contractive mappings which admit discontinuity atthe fixed point (see Rhoades, B. E.,Contractive definitions and continuity, Contemporary Mathematics72(1988),233–245, p. 242) in the setting of Menger PM-space.

A probabilistic Meir-Keeler type fixed point theorem whichcharacterizes metric completeness