ON SOME TRIANGULAR INEQUALITIES AND APPLICATIONS IN 2-FUZZY METRIC SPACES
The aim of this paper is to study some level forms of triangular inequality of 2-fuzzy metric spaces which will be useful for application to fixed point problems. For this aim, we first define the concept of 2-fuzzy pre-metric spaces that have weaker axioms than 2-fuzzy metric spaces with the fundam...
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| Published in | TWMS journal of applied and engineering mathematics Vol. 13; no. 2; p. 480 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Istanbul
Turkic World Mathematical Society
01.04.2023
Elman Hasanoglu |
| Subjects | |
| Online Access | Get full text |
| ISSN | 2146-1147 2146-1147 |
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| Abstract | The aim of this paper is to study some level forms of triangular inequality of 2-fuzzy metric spaces which will be useful for application to fixed point problems. For this aim, we first define the concept of 2-fuzzy pre-metric spaces that have weaker axioms than 2-fuzzy metric spaces with the fundamental properties. Then, we investigate the level form inequalities in 2-fuzzy metric spaces equvalent to the triangular inequalities of 2-fuzzy metric spaces by also analyzing the conditions under in which these are provided. Finally, we prove a fixed point theorem for 2-fuzzy metric spaces by considering the obtained level forms of triangular inequalities. Keywords: Fuzzy number, 2-fuzzy metric space, triangular inequality, fixed point theorem. AMS Subject Classification: 03E72, 47H10, 54E35. |
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| AbstractList | The aim of this paper is to study some level forms of triangular inequality of 2-fuzzy metric spaces which will be useful for application to fixed point problems. For this aim, we first define the concept of 2-fuzzy pre-metric spaces that have weaker axioms than 2-fuzzy metric spaces with the fundamental properties. Then, we investigate the level form inequalities in 2-fuzzy metric spaces equvalent to the triangular inequalities of 2-fuzzy metric spaces by also analyzing the conditions under in which these are provided. Finally, we prove a fixed point theorem for 2-fuzzy metric spaces by considering the obtained level forms of triangular inequalities. Keywords: Fuzzy number, 2-fuzzy metric space, triangular inequality, fixed point theorem. AMS Subject Classification: 03E72, 47H10, 54E35. The aim of this paper is to study some level forms of triangular inequality of 2-fuzzy metric spaces which will be useful for application to fixed point problems. For this aim, we first define the concept of 2-fuzzy pre-metric spaces that have weaker axioms than 2-fuzzy metric spaces with the fundamental properties. Then, we investigate the level form inequalities in 2-fuzzy metric spaces equvalent to the triangular inequalities of 2-fuzzy metric spaces by also analyzing the conditions under in which these are provided. Finally, we prove a fixed point theorem for 2-fuzzy metric spaces by considering the obtained level forms of triangular inequalities. The aim of this paper is to study some level forms of triangular inequality of 2-fuzzy metric spaces which will be useful for application to fixed point problems. For this aim, we rst de ne the concept of 2-fuzzy pre-metric spaces that have weaker axioms than 2-fuzzy metric spaces with the fundamental properties. Then, we investigate the level form inequalities in 2-fuzzy metric spaces equvalent to the triangular inequalities of 2-fuzzy metric spaces by also analyzing the conditions under in which these are provided. Finally, we prove a fixed point theorem for 2-fuzzy metric spaces by considering the obtained level forms of triangular inequalities. |
| Audience | Academic |
| Author | Aygun, Halis Guner, Elif |
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| Copyright | COPYRIGHT 2023 Turkic World Mathematical Society 2023. This work is licensed under http://creativecommons.org/licenses/by-nc/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
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| SubjectTerms | Axioms Fixed points (mathematics) Fuzzy algorithms Fuzzy logic Fuzzy systems Inequalities Inequalities (Mathematics) Mathematics Metric space Metric spaces |
| Title | ON SOME TRIANGULAR INEQUALITIES AND APPLICATIONS IN 2-FUZZY METRIC SPACES |
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