Multivalued generalizations of fixed point results in fuzzy metric spaces

Abstract

This paper attempts to prove fixed and coincidence point results in fuzzy metric space using multivalued mappings. Altering distance function and multivalued strong {bn}-fuzzy contraction are used in order to do that. Presented theorems are generalization of some well known single valued results. Two examples are given to support the theoretical results.

Some Fixed Point Theorems of Ćirić Type in Fuzzy Metric Spaces

“…Suppose that x * = f x * , y * = f y * and x * = y * . Condition (13) with x = x * , y = y * leads to the contradiction:…”

“…One of the most cited generalizations of the Banach contraction principle in probabilistic metric spaces is byĆirić [11]. More information about the fuzzy and probabilistic metric spaces, as well as fixed point theory in these spaces, can be found in [12][13][14][15][16][17][18].…”

Extended Fuzzy Metrics and Fixed Point Theorems

“…The inconvenience is due to the t-parameter and its relevance in the triangle inequality defined in a fuzzy metric space. In the last few years, several authors have contributed to the study of such topic, adapting classical fixed point theorems to the fuzzy context (see, for instance, [9,10,[18][19][20][21]). The most of them must demand an extra condition on the fuzzy metric to get fixed point.…”

Determining fuzzy distance through non-self fuzzy contractions

“…The fuzzy metric space on which we deduce our results is as in George et al [10]. Due to its special features, it has become the platform of several extensions of metric related studies [1,3,4,6,7,11,12,13,19]. The problem sought to be considered here is essentially a global optimization problem which is solved by transforming it to a problem of finding the optimal approximate solution to a fixed point equation for a non-self contraction defined by use of two control functions.…”