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

Article type: Research Article

Authors: Choudhary, Anu^a | Raj, Kuldip^a | Mursaleen, M.^{b; c; *}

Affiliations: [a] School of Mathematics, Shri Mata Vaishno Devi University, Katra, J & K, India | [b] Al-Qaryah, Doharra, Aligarh, India | [c] Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung, Taiwan

Correspondence: [*] Corresponding author. M. Mursaleen. E-mail: [email protected].

Note: [] 2010 Mathematics Subject Classification. 40A05, 40A30, 46A45, 03E72

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 Δur- convergent is (C,1,1)Δur- 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 Δur- Hardy type and Δur- slowly oscillating Tauberian condition. Finally by using these new slowly oscillating and Hardy-type Tauberian conditions, we explore some relations between (C,1,1)Δur- summable and Δur- convergent double fuzzy number sequences.

Keywords: Fuzzy number, difference operator, double sequences, Tauberian theorem, (C, 1, 1)- summability

DOI: 10.3233/JIFS-202921

Journal: Journal of Intelligent & Fuzzy Systems, vol. 40, no. 6, pp. 11799-11808, 2021