Korovkin type approximation theorems via power series method

Abstract

In this paper we consider power series method which is also member of the class of all continuous summability methods. The power series method includes Abel method as well as Borel method. We investigate, using the power series method, Korovkin type approximation theorems for the sequence of positive linear operators defined on C[a, b] and \(L_{q}[a,b]\), \(1\le q<\infty \), respectively. We also study some quantitative estimates for \(L_{q}\) approximation and give the rate of convergence of these operators.