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