In classical complex analysis, the theorems of Weierstrass, Montel and Hurwitz are of great use in very many contexts. The main goal of the present paper is to relax their strong hypotheses via the concept of A-statistical convergence, where A is a nonnegative regular summability matrix. The A-statistical convergence method is defined in the following way. Let A := [ajn] (j, n ∈ N := {1, 2, 3, ...

In this paper, we establish a new theorem on | A, pn |k summability factors of Fourier series using matrix transformation, which generalizes a main theorem of Bor [6] on ∣∣N̄, pn∣∣k summability factors of Fourier series. Also some new results have been obtained.

Many sequence spaces arise from different concepts of summability. Recent results obtained by Altay, Başar and Malkowsky [2] are related to strong Cesàro summability and boundedness. They determined β−duals of the new sequence spaces and characterized some classes of matrix transformations on them. Here, we will present new results supplementing their research with the characterization of class...

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.

p . It follows that inequality (1.2) holds for any a ∈ lp when U1/p ≥ ||C||p,p and fails to hold for some a ∈ lp when U1/p < ||C||p,p. Hardy’s inequality thus asserts that the Cesáro matrix operator C, given by cn,k = 1/n, k ≤ n and 0 otherwise, is bounded on l p and has norm ≤ p/(p−1). (The norm is in fact p/(p− 1).) We say a matrix A = (an,k) is a lower triangular matrix if an,k = 0 for n < k...

p . It follows that inequality (1.2) holds for any a ∈ lp when U1/p ≥ ||C||p,p and fails to hold for some a ∈ lp when U1/p < ||C||p,p. Hardy’s inequality thus asserts that the Cesáro matrix operator C, given by cn,k = 1/n, k ≤ n and 0 otherwise, is bounded on l p and has norm ≤ p/(p−1). (The norm is in fact p/(p− 1).) We say a matrix A = (an,k) is a lower triangular matrix if an,k = 0 for n < k...

when un = 22"-o a-inUi for all ra^O. If the sequence to sequence transformation associated with A is such that [u/[ ] exists and converges whenever [un] converges we call A a K matrix. If [uJ ] exists and converges to limn,,, un whenever this limit exists we call A a T matrix. Similar names for the series to sequence and the series to series matrices are TCi, 7\ and K2, T2 matrices respectively...