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In this study, we deal with some new vector valued multiplier spaces    $S_{G_{h}}(\sum_{k}z_{k})$  S G h ( ∑ k z k ) and    $S_{wG_{h}}(\sum_{k}z_{k})$  S w G h ( ∑ k z k ) related with    $\sum_{k}z_{k}$  ∑ k z k in a normed space  Y . Further, we obtain the completeness of these spaces via weakly unconditionally Cauchy series in  Y  and    $Y^{*}$  Y ∗ . Moreover, we show that if    $\sum_{k}z_{k}$  ∑ k z k is unconditionally Cauchy in  Y , then the multiplier spaces of    $G_{h}$  G h -almost convergence and weakly    $G_{h}-$  G h − almost convergence are identical. Finally, some applications of the Orlicz–Pettis theorem with the newly formed sequence spaces and unconditionally Cauchy series    $\sum_{k}z_{k}$  ∑ k z k in  Y  are given.

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