Weighted almost convergence and related infinite matrices

Abstract

Abstract The purpose of this paper is to introduce the notion of weighted almost convergence of a sequence and prove that this sequence endowed with the sup-norm ∥ ⋅ ∥ ∞ ${\Vert \cdot \Vert } _{\infty}$ is a BK-space. We also define the notions of weighted almost conservative and regular matrices and obtain necessary and sufficient conditions for these matrix classes. Moreover, we define a weighted almost A-summable sequence and prove the related interesting result.

Keywords

• almost convergence
• weighted almost convergence
• regular matrix