In this paper two generalized theorems on the degree of approximation of conjugate functions belonging to the Lipschitz classes of the type Lipα, 0 < α ≤ 1, and W (Lp, ξ(t)) are proved. The first one… (More)

In this paper we obtain some sufficient conditions on |N, pn, qn|k summability of an orthogonal series. These conditions are expressed in terms of the coefficients of the orthogonal series. Also,… (More)

In this paper we prove analogous theorems like Leindler’s [3] using the so-called A-transform of theB-transform of the partial sums of Fourier series. In addition, more than two such transforms are… (More)

Abstract. In this paper we have studied p-th power integrability of functions sinxg(x) and sinxf(x) with a weight, where g(x) and f(x) denote the formal sum functions of sine and cosine trigonometric… (More)

In this paper we prove that the condition 2n ∑ k=[ 2 ] kλk |n− k|+ 1 = o(1) (= O(1)) , for r = 0, 1, 2, . . . , is necessary for the convergence of the r − th derivative of the Fourier series in the… (More)

The class of convex sequences has important applications in several branches of mathematics as well as their generalizations. In this paper, we have introduced two new classes of convex sequences,… (More)

In this paper, we prove two theorems on ∣A∣k, 1 ≤ k ≤ 2, summability of orthogonal series. The first one gives a sufficient condition under which an orthogonal series is absolutely summable almost… (More)

In this paper condition of integrability of cosine trigonometric series with coe¢ cients of bounded variation of order p is obtained. The results generalize some previous results of Telyakovski1⁄4¬.… (More)