Double sequences with ideal convergence in fuzzy metric spaces

Abstract

We show ideal convergence ($ I $-convergence), ideal Cauchy ($ I $-Cauchy) sequences, $ I^* $-convergence and $ I^* $-Cauchy sequences for double sequences in fuzzy metric spaces. We define the $ I $-limit and $ I $-cluster points of a double sequence in these spaces. Afterward, we provide certain fundamental properties of the aspects. Lastly, we discuss whether the phenomena should be further investigated.