Karakus, MahmutBasar, Feyzi2025-05-102025-05-1020191578-73031579-150510.1007/s13398-019-00701-92-s2.0-85068745259https://doi.org/10.1007/s13398-019-00701-9https://hdl.handle.net/20.500.14720/13565Karakus, Mahmut/0000-0002-4468-629XIn this study, we give a slight generalization of almost convergence and introduce some new multiplier spaces associated to a series k xk in a normed space X by means of this new summability method. We also obtain some characterizations of completeness and barrelledness of the spaces through weakly unconditionally Cauchy series in X and X *, respectively. Finally, we give a version of the Orlicz-Pettis theorem, as an application of this new method and an unconditionally convergent series k xk in a normed space X.eninfo:eu-repo/semantics/closedAccessAlmost ConvergenceWuc SeriesUc SeriesOrlicz-Pettis TheoremArticle