## ON SOME TRIANGULAR INEQUALITIES AND APPLICATIONS IN 2-FUZZY METRIC SPACES

## ON SOME TRIANGULAR INEQUALITIES AND APPLICATIONS IN 2-FUZZY METRIC SPACES

*E. Güner, H. Aygün*

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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 xed 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 xed 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, xed point theorem.