A Contraction Theorem in Menger Probabilistic Metric Spaces

Completeness in Probabilistic Metric Spaces

The idea of probabilistic metric space was introduced by Menger and he showed that probabilistic metric spaces are generalizations of metric spaces. Thus, in this paper, we prove some of the important features and theorems and conclusions that are found in metric spaces. At the beginning of this paper, the distance distribution functions are proposed. These functions are essential in defining p...

Generalized Distance and Common Fixed Point Theorems in Menger Probablistic Metric Spaces

Coupled common fixed point theorems for $varphi$-contractions in probabilistic metric spaces and applications

In this paper, we give some new coupled common  fixed point theorems for probabilistic $varphi$-contractions  in Menger probabilistic metric spaces.  As applications of the main results, we obtain some coupled common fixed point theorems in usual metric spaces and fuzzy metric spaces. The main results of this paper improvethe corresponding results given by some authors. Finally, we give one exa...

Nonlinear contraction theorems in probabilistic spaces

In this paper first we prove a common fixed point theorem in Menger probabilistic metric spaces. Then we present a nonlinear contraction case of Jungck’s common fixed point theorem in Menger probabilistic metric spaces. Finally, we prove a common fixed point theorem for six self-maps in a Menger probabilistic metric space. 2007 Elsevier Inc. All rights reserved.

Some Fixed Point Results in Menger Spaces Using a Control Function

Here we prove a probabilistic contraction mapping principle in Menger spaces. This is in line with research in fixed point theory using control functions which was initiated by Khan et al. [Bull. Austral. Math. Soc., 30(1984), 1-9] in metric spaces and extended by Choudhury et al. [Acta Mathematica Sinica, 24(8) (2008), 1379-1386] in probabilistic metric spaces. An example has also been constru...