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.

In this paper, a main theorem dealing with | C, 1 |k summability factors has been generalized under more weaker conditions for | C,α, β |k summability factors. This theorem also includes some new results. Mathematics Subject Classification 2000: 40D15, 40F05, 40G05, 40G99.

Purpose: The purpose of the present paper is to study the product (N, pn) (C, 1) summability of a sequence of Fourier coefficients which extends a theorem of Prasad. Methods: We use Np. C 1 summability methods with dropping monotonicity on the generating sequence {pn − k} (that is, by weakening the conditions on the filter, we improve the quality of digital filter). Results: Let Bn(x) denote th...

Abstract The concept of Vilenkin–Lebesgue points was introduced in [12], where the almost everywhere convergence Fejer means Vilenkin–Fourier series proved. In this paper, we present a different (and simpler) approach to prove similar result, which can be used that corresponding result holds also more general context, namely for regular Norlund and T -means.

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 study we introduce the concepts of statistical convergence of order β and strong p−Cesàro summability of order β for sequences of fuzzy numbers. Also, we give some relations between the statistical convergence of order β and strong p−Cesàro summability of order β and construct some interesting examples.

the object of this paper is to establish a summability factor theorem for summabilitya, , k  1 k  where a is the lower triangular matrix with non-negative entries satisfying certain conditions.

we obtain sufficient conditions for the series σanλn to be absolutely summable of order k by atriangular matrix.

In this work we introduce and investigate the ideas of statistical Riemann integrability, summability, Lebesgue integrability summability via deferred weighted mean. We first establish some fundamental limit theorems connecting these beautiful potentially useful notions. Furthermore, based upon our proposed techniques, Korovkin-type approximation with algebraic test functions. Finally, present ...

Summability is an important concept in sequence spaces. One summability strongly Cesaro summable. In this paper, we study a subset of the set all vector-valued 2-modular space. Some facts that investigated paper include linearity, existence modular and completeness with respect to these modular.