Some spaces of Summability for Triple Sequences of Fuzzy Numbers

ABSTRACT: In this study, I extend classical concepts to triple sequences of fuzzy numbers, represented by  in order to give a fresh framework for understanding summability spaces. Inspired by the growing interest in multidimensional sequence spaces and the use of fuzzy analysis in uncertain settings, I provide a generalized triple difference operator  which is the basis for constructing a number of novel forms of summability and convergence. Specifically, I study statistically convergent sequences, lacunary statistically convergent sequences,  -lacunary strongly summable sequences, and -Cesàro strongly summable sequences in the triple fuzzy scenario. I build a number of inclusion relations between the related function spaces, which are constructed and designated appropriately. Additionally, I demonstrate that some of these spaces are complete metric spaces, expanding previous findings in the theory of fuzzy number sequences to a more flexible and broad framework. The findings of this work not only generalize existing summability techniques but also lay the groundwork for future research in multidimensional sequence analysis and fuzzy approximation.

KEYWORDS: Triple sequences, fuzzy numbers, generalized difference operator lacunary summability, Cesàro summability, statistical convergence, completeness.