On the extensions of the almost convergence idea and core theorems

Abstract

The sequence spaces rf and rf0, more general and comprehensive than the almost convergent sequence spaces f and f0, were introduced by Zararsız and Şengönül in [Z. Zararsız, M. Şengönül, Doctoral Thesis, Nevşehir, (2015)]. The purpose of the present paper is to study the sequence spaces brf and brf0, that is, the sets of all sequences such that their B(r;s) transforms are in rf and rf0 respectively. Furthermore, we determine the β-and γ- duals of brf, we show that there exists a linear isomorphic mapping between the spaces rf and brf, and between rf0 and brf0, respectively, and provide some matrix characterizations of these spaces. Finally, we introduce the BRB-core of a complex valued sequence and prove some theorems related to this new type of core.