Abstract
The main aim of the current paper is the investigation of possibilities for improvements and generalizations contractive condition of Ćirić in the fuzzy metric spaces. Various versions of fuzzy contractive conditions are studied in two directions. First, motivated by recent results, more general contractive conditions in fuzzy metric spaces are achieved and secondly, quasi-contractive type of mappings are investigated in order to obtain fixed point results with a wider class of t-norms.
Highlights
Introduction and PreliminariesThe Banach contraction principle [1] is usually taken as a starting point for many studies in the fixed point theory
The principle is observed in various types of metric spaces, as well as different generalizations of it
One of the most cited generalizations of the Banach contraction principle in probabilistic metric spaces is by Ćirić [11]
Summary
Introduction and PreliminariesThe Banach contraction principle [1] is usually taken as a starting point for many studies in the fixed point theory. In [11], a fixed point results in the probabilistic metric spaces with the following generalization of the Banach’s contraction principle: FTu,Tv (qx ) ≥ min{ Fu,v ( x ), Fu,Tu ( x ), Fv,Tv ( x ), Fu,Tv (2x ), Fv,Tu (2x )}, (1)
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