DEMONSTRATIO MATHEMATICA Vol. XXXVI No 4 2003 Oktay Duman STATISTICAL APPROXIMATION FOR PERIODIC FUNCTIONS Abstract. In this paper we study a Korovkin type approximation theorem for positive linear operators on the space of all 27r-periodic and continuous functions on the whole real axis via ^-statistical convergence. 1. Introduction The approximation theory which has a close relationship with other branches of mathematics has been used in the theory of polynomial approxi- mation and various domains of functional analysis [1], in numerical solutions of differential and integral operators [16], in the studies of the interpolation operator of Hermit-Fejer [2], [3], [4], [5] and the partial sums of Fourier series [17]. In recent years some Korovkin type approximation theorems have been studied via the concept of statistical convergence [13]. In the present paper using A—statistical convergence we study the approximation properties of sequence of positive linear operators on the space of all 27r—periodic and continuous functions on the whole real axis. Now we recall the concept of A—statistical convergence. Let A := (a n k), n, k = 1,2,..., be an infinite summability matrix. For a given sequence x := (xfc), the A—transform of x, denoted by Ax := ((Ax) n ), is given by oo (Ax) n := ^ ] &nk x ki k=1 provided the series converges for each n. A is said to be regular if Yim n (Ax) n = L whenever limx = L [14]. Then lim n = 0 for all k € N. This research was supported by the Scientific and Technical Research Council of Turkey. Key words and phrases: A—statistical convergence, sequence of positive linear opera- tors, the Korovkin type theorem. 1991 Mathematics Subject Classification: 41A25, 41A36.