On certain spaces of double sequences by de la Vallée-Poussin mean

Abstract

In this paper, we introduce some [Formula: see text]-convergence spaces of double difference sequences of interval numbers with Musielak–Orlicz function [Formula: see text] over [Formula: see text]-normed spaces. We also make an effort to study some topological properties and inclusion relations between these spaces. Furthermore, we study [Formula: see text]-statistical convergence of double difference sequences of interval numbers.

Orlicz strongly convergent sequences with some applications to Fourier series and statistical convergence

“…It is well known that the metric of any linear metric space is given by some total paranorm (see [33], Theorem 10.4.2, P-183). For more details about this type of sequence spaces (see [1], [4], [22], [24], [25], [26], [27], [28], [32]) and [5] - [19] references therein.…”