On ?-contractions in probabilistic and fuzzy metric spaces
In this paper, by means of weakening conditions of the gauge function ?, a new fixed point theorem for probabilistic ?-contraction in Menger probabilistic metric spaces with a t-norm of H-type is established. This theorem improves and generalizes the recent results of ?iri? (2010) [4], Jachymski (2010) [12] and Xiao et al. (2013) [25]. By using the theorem, we also obtain some important corollaries and the fixed point theorems for ?-contraction in fuzzy metric spaces.
?-contraction fuzzy metric space fixed point menger probabilistic metric space