On Approximation of a Function by Generalized Nörlund Summability of Its Fourier Series

In the present innovative pursuit, the generalized Nörlund summability method, that is, the (N, c, d) summation process of Fourier series of f (x) as well defined by Borwein [4] has been invoked to approximate the function f (x) belonging to Lip M α (0 < α < 1 ) and M being some constant. Here it is worth-emphasising that not only mere approximation, but also the constants appeared in the process of evaluating the integrals have meticulously been determined by us. On account of being the generalized Nörlund summability, it essentially covers the (C, 1), the (C, α) and the (N, p n ) summation processes, etc. and therefore, includes previous results due to Alexits [2], Bernstein [3], Dubey and Kumar [6], Holland et al., [9] and Sing [11].