Some new Lacunary strong convergent vector-valued multiplier difference sequence spaces defined by a Musielak-Orlicz function

Abstract: In the present paper we introduce some vector-valued multiplier difference sequence spaces defined by a Musielak-Orlicz function, concepts of lacunary convergence and strong $(A,u)$-convergence, where $A = (a_{ik})$ is an infinite matrix of complex numbers and $u = (u_i)$ be any sequence of strictly positive real numbers. We also make an effort to study some topological properties and some inclusion relations between these spaces.

Keywords: Lacunary Sequence, paranorm, Orlicz function, Musielak-Orlicz function

Classification (MSC2000): 40A05; 40C05 40D25

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