Inclusion Theorem Between The Spaces Generated By Musielak-φ Function

Abstract

Let X and G = (gi) respectively be a Banach space and a sequence of Musielak-φ function which is the generalization of Musielak-Orlicz function. Introducing the space of all X-valued sequences generated by Musielak-φ function, denoted by E∃(X,G), we investigate the sufficient and necessary condition for the inclusion relation of E∃(X,G) ⊂ F(X) and E(X) ⊂ E∃(X,G) where E ∈ {ℓ∞, ℓ1, c0} and F ∈ {ℓ∞, c0}.