Karakus, MahmutBasar, Feyzi2025-05-102025-05-1020220354-518010.2298/FIL2218347K2-s2.0-85146816852https://doi.org/10.2298/FIL2218347Khttps://hdl.handle.net/20.500.14720/14321In the present paper, we give a new characterization of unconditional convergent series and give some new versions of the Orlicz-Pettis theorem via FQ s-family and a natural family F with the separation property S1 through wRp -summability which may be considered as a generalization of the well-known strong p-Ces`aro summability. Among other results, we obtain a new (weak) compactness criteria for the summing operator.eninfo:eu-repo/semantics/openAccessArticle