In this paper we have proved two theorems concerning an inclusion between two absolute summability methods by using any absolute summability factor.

The degree of approximation of a function f belonging to Lipschitz class by the Cesàro mean and f ∈ Hα by the Fejér means has been studied by Alexits [4] and Prössdorf [7] respectively. But till now no work seems to have been done to obtain best approximation of functions belonging to generalized Zygmund class, Z (w) r , (r ≥ 1) by product summability means of the form (∆.E1). Z (w) r class is ...

In this paper we have proved some theorems on weighted mean summability method by using analytical and summability techniques, which also extends the well known result of Hardy on the Cesàro summability.

in this paper, the notion of n, pn - summability to generalize the concept of statisticalconvergence is used. we call this new method weighted statistically convergence. we also establish itsrelationship with statistical convergence, c,1-summability and strong   n n, p -summability.

In this paper we present some results on convergence and summability of oneand multi-dimensional trigonometric andWalsh-Fourier series. The Fejér and Cesàro summability methods are investigated. We will prove that the maximal operator of the summability means is bounded from the corresponding classical or martingale Hardy space Hp to Lp for some p > p0. For p = 1 we obtain a weak type inequalit...

We have established a relation between θ−|R,pn|k and θ−|R,qn|k summability methods, k > 1, which generalizes a result of Sunouchi (1949) on |R,pn| and |R,qn| summability methods.