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

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Section: Introductionmentioning

confidence: 99%

“…Since the symmetric condition is not satisfied in the fuzzy semi-metric space, three kinds of limit concepts will also be considered in this paper by referring to Wu [14]. In this section, we shall study the consistency of limit concepts in the induced topologies, which was not addressed in Wu [13].…”

mentioning

confidence: 99%

Fuzzy Semi-Metric Spaces

2018

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“…To prove Part (iv), using Part (iii) of Proposition 1 and (4) and (8) in the fourth observation of Remark 1, we have…”

mentioning

confidence: 98%

“…Wu [7] studied the so-called fuzzy semi-metric space without assuming the symmetric condition in which four forms of triangle inequalities are considered. The common coincidence points and common fixed points in fuzzy semi-metric spaces were also studied in Wu [8].…”

mentioning

confidence: 99%

Convergence in Fuzzy Semi-Metric Spaces

2018

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The convergence using the fuzzy semi-metric and dual fuzzy semi-metric is studied in this paper. The infimum type of dual fuzzy semi-metric and the supremum type of dual fuzzy semi-metric are proposed in this paper. Based on these two types of dual fuzzy semi-metrics, the different types of triangle inequalities can be obtained. We also study the convergence of these two types of dual fuzzy semi-metrics.

“…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.