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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)
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.
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.