Abstract
We introduce some vector-valued sequence spaces defined by a Musielak-Orlicz function and the concepts of lacunary convergence and strong (A)-convergence, whereA=(aik)is an infinite matrix of complex numbers. We also make an effort to study some topological properties and some inclusion relations between these spaces.
Highlights
Introduction and PreliminariesAn Orlicz function M : [0, ∞) → [0, ∞) is convex and continuous such that M(0) = 0, M(x) > 0 for x > 0
We introduce some vector-valued sequence spaces defined by a Musielak-Orlicz function and the concepts of lacunary convergence and strong (A)-convergence, where A = is an infinite matrix of complex numbers
Lindenstrauss and Tzafriri [1] used the idea of Orlicz function to define the following sequence space: lM
Summary
We make an effort to study some topological properties and some inclusion relations between these spaces
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