Abstract
We propose the so-called fuzzy semi-metric space in which the symmetric condition is not assumed to be satisfied. In this case, there are four kinds of triangle inequalities that should be considered. The purpose of this paper is to study the common coincidence points and common fixed points in the newly proposed fuzzy semi-metric spaces endowed with the so-called ⋈-triangle inequality. The other three different kinds of triangle inequalities will be the future research, since they cannot be similarly investigated as the case of ⋈-triangle inequality.
Highlights
The topic of probabilistic metric space has been studied for a long time
In order to realize the development and basic idea of probabilistic metric space, we may refer to Schweizer and Sklar [1,2,3], Hadžić and Pap [4] and Chang et al [5]
The so-called Menger space is a special kind of probabilistic metric space
Summary
The topic of probabilistic metric space has been studied for a long time. In order to realize the development and basic idea of probabilistic metric space, we may refer to Schweizer and Sklar [1,2,3], Hadžić and Pap [4] and Chang et al [5]. We shall consider the so-called fuzzy semi-metric space. In this paper, using the four different kinds of triangle inequalities, we shall study the common fixed points in fuzzy semi-metric spaces. We investigate the common coincidence points in fuzzy semi-metric spaces.
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