Approximation of a Continuous Function by a Sequence of Convolution Operators via a Matrix Summability Method Using Ideals

Abstract

In this paper, in the line of Duman [7], we deal with Korovkin type approximation theory for a sequence of positive convolution operators defined on $C[a,b]$, the Banach space of all real valued continuous functions on $[a,b]$ endowed with the supremum norm $||f||=\sup_{x\in [a,b]}|f(x)|$ for $f\in C[a,b]$, based on the notion of $A^\mathcal {I}$-summability. We construct an example to exhibit that the main result is more generalized than its statistical $A$-summable version. We also study the rate of $A^\mathcal {I}$-summability.