Applications of Orlicz–Pettis theorem in vector valued multiplier spaces of generalized weighted mean fractional difference operators

Abstract In this study, we deal with some new vector valued multiplier spaces $S_{G_{h}}(\sum_{k}z_{k})$ SGh(?kzk) and $S_{wG_{h}}(\sum_{k}z_{k})$ xmlns:mml="http://www.w3.org/1998/Math/MathML">SwGh(?kzk) related $\sum_{k}z_{k}$ xmlns:mml="http://www.w3.org/1998/Math/MathML">?kzk in a normed space Y . Further, obtain the completeness of these via weakly unconditionally Cauchy series $Y^{*}$ xmlns:mml="http://www.w3.org/1998/Math/MathML">Y? Moreover, show that if is , then $G_{h}$ xmlns:mml="http://www.w3.org/1998/Math/MathML">Gh -almost convergence $G_{h}-$ xmlns:mml="http://www.w3.org/1998/Math/MathML">Gh? almost are identical. Finally, applications Orlicz–Pettis theorem newly formed sequence given.