In this paper we are dealing with approximation by summation integral operatos. We show the connections between the local smoothness of the approximated function and the rate of its local approximation. The direct theorem is obtained in a general case. Also, an inverse result is presented under certain conditions imposed on the sequence of operators, the most important being the commutativity of the operators and a restriction on the second order moments of the operators.
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
O. Agratini, Smoothness properties of positive summation integral operators, East Journal on Approximation, 5 (1999) no. 4, pp. 381-392.
About this paper
East Journal on approximation
Publisher DARBA (Bulgaria)
google scholar link
 O. Agratini, On a genrealized Durrmeyer operators, Bul. St. Baia-Mare 12 (1996), 21-30.
 C.K. Chui, T.X. He and L.C. Hsu, Asymptotic properties of positive summation-integral operators, J. Approx. Theory 55 (1988), 49-60.
 M.M. Derriennic, Sur l’approximation des fonctions inegrables sur [0,1] par des polynomes de Bernstein modifies, J. Approx. Theory 31 (1981), 325-343.
 M. Heilmann, Direct and converse results for operators of Baskakov-Durrmeyer type, Approx. and Appl. 5 (1989), 105-127.
 Song, Li, Local smoothness of functions and Baskakov-Durrmeyer Operators, J. Approx. Theory 88 (1997), 139-153.
 S.M. Mazhar and V. Totik, Approximaiton by modified Szasz operators, Acta Sci. Math. 49 (1985), 257-269.
 A. Sahai and G. Prasad, On simultaneous approximation by modified Lupas operator, J. Approx. Theory 45 (1985), 122-128.
 Chen Wenzhong, On the integral type Meywe-Konig and Zeller operators, Approx. Theory Appl. 2, 3 (1986), 7-18.