On ideal summability and a Korovkin type approximation theorem

Abstract

In this paper, we define and study the notion of $$I_{\lambda }$$ -convergence as a variant of the notion of ideal convergence, where $$\lambda =(\lambda _{n})$$ is a nondecreasing sequence of positive real numbers such that $$\lambda _{n+1} \le \lambda _{n}+1,\lambda _{1}=1,\lambda _{n}\rightarrow \infty (n\rightarrow \infty ).$$ We further apply this notion of summability to prove a Korovkin type approximation theorem.