DEGREE OF APPROXIMATION BY PRODUCT ( N ; pn; qn)(E; q) SUMMABILITY OF FOURIER SERIES OF A FUNCTION BELONGING TO LIPSCHITZ CLASS
SUSANTA KUMAR PAIKRAY *
Department of Mathematics, VSS University of Technology, Burla - 768018, India
*Author to whom correspondence should be addressed.
Abstract
Approximation of periodic functions by different 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 (
, pn , qn)(E, q)-summability of Fourier series of a function belonging to f ∈ Lip(ξ(t), r) class that generalizes several known results.
Keywords: Degree of approximation, fourier series, Lip((t); r)-class, (N; pn; qn)-mean, (N; pn; qn) (E; q)-mean, Lebesgue integral