Infinite matrices and absolute almost convergence

Abstract

In 1973, Stieglitz [5] introduced a notion of FB-Convergence which provided a wide generalization of the classical idea of almost convergence due to Lorentz [1]. The concept of strong almost convergence was introduced by Maddox [3] who later on generalized this concept analogous to Stieglitz's extension of almost convergence [4]. In the present paper we define absolute FB-Convergence which naturally emerges from the concept of FB-Convergence.