STRONG $F_A$-SUMMABILITY

Abstract

Let $A = (a_{nk})$ be an infinite matrix and $x =(x_k)$ an infinite sequence of complex numbers. A sequence $x$ is said to be $F_A$-summable to a number $\ell$ [ActaMath. 80(1948),167-190] if and only if $x$ is bounded and

\[\sum_{k=0}^\infty a_{nk}x_{k+p}\to \ell\]

as $n\to\infty$, uniformly for $p\ge 0$.
The object of this paper is to define strong $F_A$-summability which is a generalization of strong almost convergence due to I. J. Maddox [Math. Proc. Camb. Phil. Soc., 83 (1978), 61-64]. We also characterize the matrices which transform strong almost convergent sequences to strong $F_A$-summable sequences.