We extended a theorem of Mishra and Srivastava (1983–1984) on |C,1|k summability factors, using almost increasing sequences, to |N̄,pn|k summability under weaker conditions.

Some recent results on a general summability method, on the so-called θ-summability is summarized. New spaces, such as Wiener amalgams, Feichtinger’s algebra and modulation spaces are investigated in summability theory. Sufficient and necessary conditions are given for the norm and a.e. convergence of the θ-means.

In this paper, we first introduce the notion of summability of an infinite set of vectors of real Hilbert space, without using index sets. Further we introduce the notion of weak summability, which is weaker than that of summability. Then, several statements for summable sets and weakly summable ones are proved. In the last part of the paper, we give a necessary and sufficient condition for sum...

and po.biu, v), («, v), has been considered by a number of writers. Gergen and Littauer [4, Theorems IV and V] have treated the problem of the boundedness, and convergence in the Pringsheim sense, of ...

If B is a summability matrix, then the submethod Bλ is the matrix obtained by deleting a set of rows from the matrix B. Comparisons between Euler-Knopp submethods and the Borel summability method are made. Also, an equivalence result for convolution submethods is established. This result will necessarily apply to the submethods of the Euler-Knopp, Taylor, Meyer-König, and Borel matrix summabili...

This paper is a study of summability methods that are based on the Riemann Zeta function. A limitation theorem is proved which gives a necessary condition for a sequence x to be zeta summable. A zeta summability matrix Z associated with a real sequence is introduced; a necessary and sufficient condition on the sequence such that Z maps 11 to 11 is established. Results comparing the strength of ...

Abstract A remarkable result on summability states that the statistical convergence and strong Cesàro are closely connected. Given a modulus function f , we will establish double sequence is -strong convergent always -statistically convergent. The converse, in general, false even for bounded sequences. However, characterize analytically functions which converse of this remains true. results pap...

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.

Using an almost increasing sequence, a result of Mazhar (1977) on |C,1|k summability factors has been generalized for |C,α;β|k and |N̄,pn;β|k summability factors under weaker conditions. 2000 Mathematics Subject Classification. 40D15, 40F05, 40G05.

A theorem on local property of |N̄,pn|k summability of factored Fourier series, which generalizes some known results, and also a general theorem concerning the |N̄,pn|k summability factors of Fourier series have been proved.