Approximation of Signals by Product Summability Transform

The theory of approximation is a very extensive field which has various applications in pure and applied mathematics. Broadly speaking, Signals are treated as functions of one variable and images are represented by functions of two variables. The present study deals with the new theorem on the degree of approximation of a Signal associated with Fourier series and belonging to the generalized weighted W(Lr, ξ(t)) (r≥1, t>0)- class by product summability (C, 1) (E, q) method, where ξ (t) is non-negative and non-decreasing function of t. The main result obtained in this study generalizes some well-known results in this direction. The class W(Lrξ(t)) (r≥1, t>0), we have used here in the main theorem includes the Lip (ξ(t)), Lip (a, r) and Lip a classes.