A modified Fejér and Jackson summability method with respect to orthogonal polynomials

Abstract

Let {P n } ∞ n=0 be an orthogonal polynomial system on the real line with respect to a measure µ with compact support S. Following the classical methods, we define a modified Fejér and Jackson summability method for Fourier series with respect to {P n } ∞ n=0 . There is a discussion for ultraspherical polynomials. Moreover, we give error estimates for positive summability methods.