On the $K_r$ -core of complex sequences and the absolute equivalence of summability matrices

Abstract

The $K_r$-core of a complex valued sequence has been introduced in [5]. In this paper, we have determined a class of matrices such that $K_r - core (Ax)\subseteq K_r - core (x)$ hold for all $x\in 1\infty$. Also; we have defined a new type of absolute equivalence, r - absolute equivalence, and characterized these type of matrices.