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

Fuzzy set theory has entered into a large variety of disciplines of sciences,technology and humanities having established itself as an extremely versatileinterdisciplinary research area. Accordingly different notions of fuzzystructure have been developed such as fuzzy normed linear space, fuzzytopological vector space, fuzzy sequence space etc. While reviewing theliterature in fuzzy sequence space, we have seen that the notion of Tauberiantheorems for the Euler-N\"{o}rlund mean-convergent sequences of fuzzy numbershas not been developed. In the present paper, we introduce some new conceptsabout statistical convergence of sequences of fuzzy numbers. The main purposeof this paper is to study Tauberian theorems for the Euler-N\"{o}rlundmean-convergent sequences of fuzzy numbers and investigate some other kind ofconvergences named Euler-N\"{o}rlund mean-level convergence so as to fill upthe existing gaps in the literature. The results which we obtained in thisstudy are much more general than those obtained by others.

Keywords:

Statistical convergence , Tauberian theorems , Fuzzy numbers