A = (ank) be a regular summability matrix. In the present paper we deal with subspaces of space A?statistically convergent sequences obtained by rate at which A?statistical limit tends to zero. We prove that sequence is A?strongly if and only it A?uniformly integrable o (an) where positive nonincreasing sequence. also make link between A?strong convergence A?distributional (an). Finally, as an ...

Many concepts and theories in functional analysis have turned out to be powerful and widely used tools in operator theory, in particular in the theory of matrix transformations between sequences spaces in summability. We give an introduction to the basic theory of FK, BK, AK and AD spaces, the various types of dual spaces of sequence spaces, and apply the general results to the characterisation...

Abstract In this paper we generalize the space $\hat{\ell }_{k}$ ℓ ˆ k of absolutely almost convergent series (J. Math. Anal. Appl. 161:50–56, 1991) via weighted mean transformations. We study some inclusion relations and their ...

In this paper, we continue our investigations in line of our recent papers, Savas and Das [16] and Das, Savas and Ghosal [5]. We introduce the notion of AI statistical convergence which includes the new summability methods studied in [16] and [5] as special cases and make certain observations on this new and more general summability method.