Invariant means and lacunary sequence spaces of order (α, β)

Abstract

In this article, we use the notion of lacunary statistical convergence of order (α,β)\left(\alpha ,\beta ) to introduce new sequence spaces by lacunary sequence, invariant means defined by Musielak-Orlicz function ℳ=(ℵk){\mathcal{ {\mathcal M} }}=\left({\aleph }_{k}). We also examine some topological properties and prove inclusion relations between newly constructed sequence spaces.

Keywords

• difference sequence space
• fractional difference operator
• orlicz function
• musielak-orlicz function
• lacunary sequence
• invariant mean
• 40a05
• 40a35
• 40c05
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• 46a45