Comments on 'Fixed point theorems for \phi-contraction in probabilistic metric space'

Abstract

In this work we have shown that an affirmative answer was already given in [1, 5] to the question raised in [4] and have extended a fixed point theorem by L.Ćirić [4] to a larger class of PM spaces. In the final part of the paper we have shown that the result can be yet improved by a common fixed point theorem for a semigroups of ϕ-probabilistic contractions.

Probabilistic Generalized Metric Spaces and Nonlinear Contractions

“…Then, we discuss the relationship of some concepts of the new class 'probabilistic generalized metric space' to the classical axioms of probabilistic metric space. Finally, we show the existence and uniqueness of the fixed point for the ϕ-probabilistic contraction mapping ( [5], [14]) in a probabilistic (fuzzy) generalized metric space without the Hausdorff condition.…”

Cyclical contractive conditions in probabilistic metric spaces

“…The t-norm T M is a trivial example of t-norm of Htype.Definition 2.10 [5]. Let ϕ : [0, ∞) → [0, ∞) be a function such that ϕ(t) < t for t > 0, and f be a selfmap of a probabilistic metric space (M, F, τ).…”