Abstract
In this paper, we introduce refined notions related to convergence for sequences of functions. These include relative alpha convergence and relative continuity at a point with respect to a scale function, as localized and strict parametric variants of classical alpha convergence. Furthermore, using these new concepts, we investigate their properties and relationships among these different notions. Lastly, we give a Korovkin‐type theorem for relative alpha convergence; it will be observed that the conditions in the classical Korovkin theorem can be effectively extended.