Korovkin-type theorem which is one of the fundamental methods in approximation theory to describe uniform convergence of any sequence of positive linear operators is discussed on weighted L p spaces, 1 ≤ p < ∞ for univariate and multivariate functions, respectively. Furthermore, we obtain these types of approximation theorems by means of -summability which is a stronger convergence method than ordinary convergence. © 2013 Tuncer Acar and Fadime Dirik.