Orlicz-Lacunary convergent double sequences and their applications to statistical convergence

Document Type : Original Article

Authors

Kuldip Raj

Charu Sharma

Swati Jasrotia

School of Mathematics Shri Mata Vaishno Devi University, Katra-182320,\linebreak \indent J \& K (India)

10.22034/kjm.2021.272612.2173

Abstract

In this article, we introduce and study Orlicz lacunary convergent double sequences over $n$-normed spaces. We define the notion of $g_{2}$-statistical convergence in double sequence spaces. We study some topological and algebraic properties of newly formed sequence spaces. Some inclusion relations are also establish in this paper. Finally, we study some applications of statistical convergence in these spaces.

Keywords

$g$-statistical convergence

strongly almost convergence

$n$-norm

strongly $p$-Cesaro summability

---