Applications of Tauberian theorems for double sequences of fuzzy numbers via De La Vallée Poussin mean

Abstract

Tauberian theorem serves the purpose to recuperate Pringsheim’s convergence of a double sequence from its (C, 1, 1) summability under some additional conditions known as Tauberian conditions. In this article, we intend to introduce some Tauberian theorems for fuzzy number sequences by using the de la Vallée Poussin mean and double difference operator of order r . We prove that a bounded double sequence of fuzzy number which is Δ u r - convergent is ( C , 1 , 1 ) Δ u r - summable to the same fuzzy number L . We make an effort to develop some new slowly oscillating and Hardy-type Tauberian conditions in certain senses employing de la Vallée Poussin mean. We establish a connection between the Δ u r - Hardy type and Δ u r - slowly oscillating Tauberian condition. Finally by using these new slowly oscillating and Hardy-type Tauberian conditions, we explore some relations between ( C , 1 , 1 ) Δ u r - summable and Δ u r - convergent double fuzzy number sequences.