In the present paper, two quite new reults on the degree of approximation of a function f belonging to the class Lip(α, r), 1 ≤ r < ∞ and the weighted class W (Lr, ξ(t)), 1 ≤ r < ∞ by (C, 2)(E, 1) product operators have been obtained. The results obtained in the present paper generalize various known results on single operators.
In this paper, a quite new theorem on almost summability of Fourier-Jacobi series has been established. Our theorem extends and generalizes all previously known results of this line of work.
A good amount of work has been done on degree of approximation of functions belonging to Lipα, Lip(α, r), Lip(ξ(t), r) and W (L r , ξ(t)) classes using Cesàro and (generalized) Nörlund single summability methods by a number of researchers like Alexits , Sahney and Goel till now no work seems to have been done so far in the direction of present work.… (More)