Hausdorff Topology Induced by the Fuzzy Metric and the Fixed Point Theorems in Fuzzy Metric Spaces

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Section: Introductionmentioning

confidence: 99%

“…The Hausdorff topology induced by the fuzzy metric space was studied in Wu [13], and the concept of fuzzy semi-metric space was considered in Wu [14]. In this paper, we shall extend to study the T 1 -spaces induced by the fuzzy semi-metric spaces that is endowed with special kind of triangle inequality.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Semi-Metric Spaces

2018

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“…first component). [12]) Suppose that the t-norm * is left-continuous at 1 with respect to the first or second component. For any a ∈ (0, 1) and any p ∈ N, there exists r ∈ (0, 1) such that p times r * r * · · · * r> a.…”

Section: Fuzzy Semi-metric Spacesmentioning

confidence: 99%

“…The formal definition is given below. [12]) Let (X, M, * ) be a fuzzy quasi-metric space. Given any two elements x, y ∈ X with x = y, the concepts of finite distance are defined below.…”

Section: Auxiliary Function Based On the Supremummentioning

confidence: 99%

Common Coincidence Points and Common Fixed Points in Fuzzy Semi-Metric Spaces

2018

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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.

“…Although the space F cc (R) is not a vector space, the Hahn-Banach extension theorems on F cc (R) still can be studied by referring to Wu [7]. On the other hand, the fixed point theorems in fuzzy metric space have been studied in [8][9][10][11][12][13][14][15][16][17][18][19]. However, the fuzzy metric space is completely different from the near metric space of fuzzy numbers that is adopted in this paper.…”

Section: Introductionmentioning

confidence: 99%

Near Fixed Point Theorems in the Space of Fuzzy Numbers

2018

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Abstract:The fuzzy numbers are fuzzy sets owning some elegant mathematical structures. The space consisting of all fuzzy numbers cannot form a vector space because it lacks the concept of the additive inverse element. In other words, the space of fuzzy numbers cannot be a normed space even though the normed structure can be defined on this space. This also says that the fixed point theorems established in the normed space cannot apply directly to the space of fuzzy numbers. The purpose of this paper is to propose the concept of near fixed point in the space of fuzzy numbers and to study its existence. In order to consider the contraction of fuzzy-number-valued function, the concepts of near metric space and near normed space of fuzzy numbers are proposed based on the almost identical concept. The concepts of Cauchy sequences in near metric space and near normed space of fuzzy numbers are also proposed. Under these settings, the existence of near fixed points of fuzzy-number-valued contraction function in complete near metric space and near Banach space of fuzzy numbers are established.