Let K be a compact metric space and let denote the real Banach space of all continuous functions which are 2π‐periodic with respect to the second variable. We prove the following Korovkin‐type result: Let be a continuous algebraic separating function such that for all , and let be a sequence of positive linear operators. If uniformly with respect to and uniformly on for all , then uniformly on for every .
As a corollary we deduce: If , then uniformly on for every if and only if uniformly on for every , where and .