Some seminormed difference sequence spaces defined by a Musielak-Orlicz function over n-normed spaces

Abstract

In the present paper we introduced some seminormed difference sequence spaces combining lacunary sequences and MusielakOrlicz function M = (M k ) over n-normed spaces and examine some topological properties and inclusion relations between resulting sequence spaces.

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

“…If = = 1, = 1, and ( ) = ∀ in our difference sequence spaces defined above, then these spaces reduce to the difference sequence spaces defined by Raj et al [40]. Moreover, if we take = = 1 in our difference sequence spaces and take = 1 for all in the difference sequence spaces defined by Raj and Sharma [41], then we observe that difference sequence spaces of both the manuscripts coincide.…”

Mappings of Type Special Space of Sequences

“….} that do not contain more than number of elements and let { } be a nondecreasing sequence of positive reals such that +1 ≤ ( + 1) , for all ∈ N. Tripathy and Mahanta [6] defined and studied the following sequence space: As of late, different classes of sequences have been presented using Orlicz functions by Braha [7], Raj and Sharma Sunil [8], Raj et al [9], and many others ( [10][11][12][13]).…”

On Some Classes of Double Difference Sequences of Interval Numbers

“…Taking = 1, we get the spaces studied by Et and Ç olak [19]. For more details about sequence spaces see [20][21][22][23][24][25][26][27][28][29][30][31][32] and references therein. Quite recently, Et et al [33] defined and studied the concept of statistical convergence of order involving the notions of Δ and ideal .…”