Core Theorems in The Generalized Statistical Sense

Abstract

The main purpose of the paper is to give some results concerning with the generalized statistical core of a bounded sequence via $\mathfrak{B}$-statistical convergence where $\mathfrak{B}=(B_{i})$ is a sequence of infinite matrices. We characterize the matrix class $(st_{\mathfrak{B}}\cap X,Y)$ for certain sequence spaces $X$ and $Y$. Here $st_{\mathfrak{B}}$ is the set of all $\mathfrak{B}$-statistically convergent sequences. Finally we answer the multipliers and factorization problem for $\mathfrak{B}$-statistically convergent sequences.

Keywords

• Knopp core,generalized statistical convergence,$\mathfrak{B}$- statistical limit superior and inferior

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