On fixed point theorems involving altering distances in Menger probabilistic metric spaces

Abstract

In this paper, we show by means of an example that the results of Babačev (Appl. Anal. Discrete Math. 6:257-264, 2012) do not hold for the class of t-norms T ≤ Tp. Further, we prove a fixed point theorem for quasi-type contraction involving altering distance functions which is weaker than that proposed by Babačev but for any continuous t-norm in a complete Menger space. ©2013 Došenović et al.; licensee Springer.