Tauberian theorems for statistical Cesàro and statistical logarithmic summability of sequences in intuitionistic fuzzy normed spaces

Article type: Research Article

Authors: Yavuz, Enes^{; *}

Affiliations: Department of Mathematics, Manisa Celal Bayar University, Manisa, Turkey

Correspondence: [*] Corresponding author. Enes Yavuz, Department of Mathematics, Manisa Celal Bayar University, Manisa, Turkey. E-mail: enes.yavuz@cbu.edu.tr.

Abstract: We define statistical Cesàro and statistical logarithmic summability methods of sequences in intuitionistic fuzzy normed spaces(IFNS) and give slowly oscillating type and Hardy type Tauberian conditions under which statistical Cesàro summability and statistical logarithmic summability imply convergence in IFNS. Besides, we obtain analogous results for the higher order summability methods as corollaries. Also, two theorems concerning the convergence of statistically convergent sequences in IFNS are proved in the paper.

Keywords: Intuitionistic fuzzy normed space, tauberian theorem, cesàro and logarithmic summability methods, statistical convergence, slow oscillation

Keywords: 03E72, 40A05, 40G05, 40G15, 40E05

DOI: 10.3233/JIFS-210596

Journal: Journal of Intelligent & Fuzzy Systems, vol. 40, no. 6, pp. 12433-12442, 2021