On the extensions of the almost convergence idea and core theorems

Zararsiz, Zarife¹

¹ Department of Mathematics, Nevşehir Hacı Bektaş Veli University, 50300, Nevşehir, Turkey

Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 1, p. 112-125.

Résumé

The sequence spaces $rf$ and $rf_0$, more general and comprehensive than the almost convergent sequence spaces $f$ and $f_0$, 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 $brf_0$, that is, the sets of all sequences such that their $B(r; s)$ transforms are in $rf$ and $rf_0$ respectively. Furthermore, we determine the $\beta$- and $\gamma$- duals of brf, we show that there exists a linear isomorphic mapping between the spaces $rf$ and $brf$, and between $rf_0$ and $brf_0$ respectively, and provide some matrix characterizations of these spaces. Finally, we introduce the $B_{RB}$-core of a complex valued sequence and prove some theorems related to this new type of core.

Détail

DOI : 10.22436/jnsa.009.01.11

Classification : 40C05, 46A45, 40J05
Keywords: Almost convergence, \(\beta\)- and \(\gamma\)-duals, matrix domain of a sequence space, isomorphism, core theorem.

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