Lacunary ideal summability and its applications to approximation theorem

Abstract

An ideal I is a family of subsets of positive integers $$\mathbf {N}$$ which is closed under taking finite unions and subsets of its elements. In this paper, we define and study the notion of $$I_{\theta }$$ -convergence as a variant of the notion of ideal convergence, where $$\theta = (h_{r})$$ is a nondecreasing sequence of positive real numbers. We further apply this notion of summability to prove a Korovkin type approximation theorem.