Abstract
In this paper, we extend Caristi’s fixed point theorem in metric spaces to probabilistic metric spaces, and also, we prove some common fixed point theorems for a pair of mappings satisfying a system of Caristi-type contractions in the setting of a Menger space. Two examples are given to support the main results. Furthermore, we have functional equations as an application for the main theorem.
Highlights
Introduction andPreliminaries e theory of probabilistic metric spaces is of fundamental importance in random functional analysis especially due to its extensive applications in random differential and random integral equations
In view of the lower semicontinuity of φ, it follows that φ(p) ≤ lim inf φ α pα
We prove that p is an upper bound ofα∈I
Summary
Introduction andPreliminaries e theory of probabilistic metric spaces is of fundamental importance in random functional analysis especially due to its extensive applications in random differential and random integral equations. If c is a right lower (upper) semicontinuous function at α, it is right locally bounded below (above) at α, that is, there exists λ > 0 such that inf(c[α, α + λ]) > − ∞(sup(c[α, α + λ]) < + ∞). We always denote by D the set of all distribution functions.
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