In the present paper, using a A-summation process we give a theorem of the Korovkin type for a sequence of positive linear operators acting from a weighted space C ρ 1 into B ρ 2 . We also study the rates of convergence of these operators.

In this paper we consider power series method which is also member of the class of all continuous summability methods. The power series method includes Abel method as well as Borel method. We investigate, using the power series method, Korovkin type approximation theorems for the sequence of positive linear operators defined on C[a, b] and L q [a, b], 1 ≤ q < ∞, respectively. We also study some quantitative estimates for L q approximation and give the rate of convergence of these operators.

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In the present paper we prove a Korovkin type approximation theorem for a sequence of positive linear operators acting from a weighted space Cρ 1 into a weighted space Bρ 2 with the use of a matrix summability method which includes both convergence and almost convergence. We also study the rates of convergence of these operators.

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