DEGREE OF APPROXIMATION BY PRODUCT (¯(N,)pn, qn)(E, q) SUMMABILITY OF FOURIER SERIES OF A SIGNAL BELONGING TO Lip(α, r)-CLASS

P. Parida, S. K. Paikray, M. Dash, U. K. Misra

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Abstract

Approximation of periodic functions by dierent linear summation methods have been studied by many researchers. Further, for sharpening the estimate of errors out of the approximations several product summability methods were introduced by different investigators. In this paper a new theorem has been established on (N; pn; qn)(E; q)- summability of Fourier series of a function belonging to f 2 Lip(; r) class that generalizes several known results.

Keywords

Degree of approximation, Fourier series, Lip(; r)-class, (N; pn; qn)(E; s)- mean, Lebesgue integral.