TAUBERIAN THEOREMS FOR THE EULER-NORLUND MEAN-CONVERGENT SEQUENCES OF FUZZY NUMBERS

Abstract

Fuzzy set theory has entered into a large variety of disciplines of sciences, technology and humanities having established itself as an extremely versatile interdisciplinary research area. Accordingly different notions of fuzzy structure have been developed such as fuzzy normed linear space, fuzzy topological vector space, fuzzy sequence space etc. While reviewing the literature in fuzzy sequence space, we have seen that the notion of Tauberian theorems for the Euler-Norlund mean-convergent sequences of fuzzy numbers has not been developed. In the present paper, we introduce some new concepts about statistical convergence of sequences of fuzzy numbers. The main purpose of this paper is to study Tauberian theorems for the Euler-Norlund mean-convergent sequences of fuzzy numbers and investigate some other kind of convergences named Euler-Norlund mean-level convergence so as to fill up the existing gaps in the literature. The results which we obtained in this study are much more general than those obtained by others.