Some Seminormed Difference Sequence Spaces over n-Normed Spaces Defined by a Musielak-Orlicz Function of Order (α,β)

Abstract

We first define the notion of lacunary statistical convergence of order ( , ), and taking this notion into consideration, we introduce some seminormed difference sequence spaces over -normed spaces with the help of Musielak-Orlicz function M = ( ) of order ( , ). We also examine some topological properties and prove inclusion relations between the resulting sequence spaces.

Seminormed double sequence spaces of four-dimensional matrix and Musielak–Orlicz function

“…Quite recently, Mursaleen and Mohiuddine [ 28 , 29 ] studied the notion of ideal convergence of double sequences in probabilistic normed spaces and also gave the concept of statistically convergent and statistically Cauchy double sequences in intuitionistic fuzzy normed spaces. For more details also see [ 22 , 23 , 30 , 38 ].…”