Lacunary ideal summability and its applications to approximation theorem

An ideal I is a family of subsets of positive integers 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=(hr) is a nondecreasing sequence of positive real numbers. We further apply this notion of summability to prove a Korovkin type approximation theorem.