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We determine the degree of approximation of conjugate of a function belonging to Lip(ξ(t), p) class by matrix summability means of a conjugate series of a Fourier series. have determined the degree of approximation of a function belonging to Lip α by (C, 1), (C, δ), (N, p n), and (N, p n) means of its Fourier series. Working in the same direction Sahney and… (More)
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.
A new theorem on almost generalized Nörlund summability of conjugate series of Fourier series has been established under a very general condition. 2000 Mathematics Subject Classification. Primary 42B05, 42B08.