3 General results on summability and duality 4 3.1 Total algebras and duality . . . . . . . . . . . . . . . . . . . . . . 4 3.1.1 Series and infinite sums . . . . . . . . . . . . . . . . . . . 4 3.1.2 Summable families in Hom spaces. . . . . . . . . . . . . . 5 3.1.3 Substitutions . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2 Theorem of Cartier-Quillen-Milnor-Moore (analytic form) . ....

0. Preface. This article is a survey of certain aspects of the theory of multiple Fourier and trigonometric series. I t is by no means meant to be a complete survey; for example, it is practically disjoint with the material covered on the subject in Zygmund's book [38, Chapter 17.]. There are eight sections to this survey. §1 is the introduction. §2, §3, and §4 are expository in the sense that ...

In 2000, Kostyrko, Salat, and Wilczynski introduced and studied the concept of I-convergence of sequences in metric spaces where I is an ideal. The concept of I-convergence has a wide application in the field of Number Theory, trigonometric series, summability theory, probability theory, optimization and approximation theory. In this article we introduce the double sequence spaces     2 0 2...

A weighted mean matrix, denoted by (N , pn), is a lower triangular matrix with entries pk/Pn, where {pk} is a nonnegative sequence with p0 > 0, and Pn := ∑n k=0 pk. Mishra and Srivastava [1] obtained sufficient conditions on a sequence {pk} and a sequence {λn} for the series ∑ anPnλn/npn to be absolutely summable by the weighted mean matrix (N , pn). Bor [2] extended this result to absolute sum...

In this paper, determining the operator norm, we give certain characterizations of matrix transformations from space $ \left\vert \overline N_p^{\phi }\right\vert _{k}$, all series summable by absolute weighted mean summability method, to one classical sequence spaces $c_{0},c,l_{\infty }.$ Also, obtain necessary and sufficient conditions for each in these classes be compact establish a number ...

In this paper we introduce new Tauberian conditions for Abel summability method that include Hardy Littlewood Tauberian condition [4] as a special case. Mathematics Subject Classification: 40E05

In this paper, using a matrix summability method we obtain a Korovkin type approximation theorem for a sequence of positive linear operators defined on a modular space.

We establish sufficient conditions for summability of integrals with multiplier by $|\overline{W}, p(y)|_k$, $k \geqslant 1$, method.