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We introduce the notion of R(g, g ′ )-continuity on generalized topological spaces, which is a strong form of (g, g)-continuity. We investigate some properties and relationships among R(g, g ′ )-continuity, (g, g ′ )-continuity and some strong forms of (g, g′)-continuity.

R(g, g')-CONTINUITY ON GENERALIZED TOPOLOGICAL SPACES