FUZZY QUASI-METRIC VERSIONS OF A THEOREM OF GREGORI AND SAPENA

Abstract

We provide fuzzy quasi-metric versions of a fixed point theorem of Gregori and Sapena for fuzzy contractive mappings in G-complete fuzzy metric spaces and apply the results to obtain fixed points for contractive mappings in the domain of words. 1. Introduction and Preliminaries Fixed point theories in fuzzy metric spaces and probabilistic metric spaces are closely related. The fixed point theory of the fuzzy metric spaces was introduced by Grabiec (2), where a fuzzy metric version of the Banach contraction principle was proved. In order to obtain his theorem, Grabiec considered a notion of com- pleteness, now called G-completeness, cf. (5). Subsequently, Gregori and Sapena (5) introduced a new class of contractive mappings in G- complete fuzzy metric spaces. Recent results related to the paper of Gregori and Sapena (5) may be found in (9), (10), (11), (12), (13), (18). Unfortunately, G-completeness is a very restricting notion, and as is shown in (17), even the induced fuzzy metric space (R,M,Min), where M(x,y,t) = t