Abstract
In the present paper, we defined lacunary sequence spaces of fractional difference operator of orderα,βovern-normed spaces via Musielak-Orlicz functionM=Ik. Our aim in this paper is to study some topological properties and inclusion relation between the spacesI−NαβA,M,u,θ,Δγ,·,⋯,·0,I−NαβA,M,u,θ,Δγ,·,⋯,·, andI−NαβA,M,u,θ,Δγ,·,⋯,·∞.
Highlights
Introduction and PreliminariesThe concept of statistical convergence was introduced by Fast [1] and Schoenberg [2] independently
Many authors studied the concept of statistical convergence from the past few years we may refer to ([3–19]) and references therein
By a lacunary sequence θ = ðθrÞ, we mean a sequence of positive integers such that θ0 = 0, 0 < θr < θr+1, and φr = θr − θr−1 ⟶ ∞ as r ⟶ ∞
Summary
Introduction and PreliminariesThe concept of statistical convergence was introduced by Fast [1] and Schoenberg [2] independently. The sequence ξ = ðξkÞ is SβαðθÞ-statistically convergent (or lacunary statistically convergent of order ðα, βÞ) (see [20]) if there is a real number L such that lim α jfk r⟶∞ φr where Jr = ðθr−1, θr and φαr denotes the αth power ðφrÞα of φr, that is, φα = ðφαr Þ = ðφα[1], φα2,⋯,φαr ,⋯Þ. We write SβαðθÞ − limξk = L: The set of all SβαðθÞ-statistically Journal of Function Spaces convergent sequences is denoted by SβαðθÞ.
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