TRIGONOMETRIC APPROXIMATION OF FUNCTIONS BY HAUSDORFF-MATRIX PRODUCT OPERATORS

Abstract

In this paper, we obtain the error approximation of a function in weighted W(Lr,ξ(t)),r ≥ 1 class by Hausdorff-Matrix (∧T) product means of its Fourier series. Our main theorems generalize the results of Nigam ([18], [19]), Nigam and Sharma [20], Singh and Srivastava [28] and Lal [14]. Thus, these results become the particular cases of our theorems. Some important corollaries are also deduced from our main theorems.