Some properties of the operators defined by Lupaș

Author:

Erençin Ayşegül,Bașcanbaz-Tunca Gülen,Tașdelen Fatma

Abstract

In the present paper, we show that a subclass of the operators defined by Lupaș [12] preserve properties of the modulus of continuity function and Lipschitz constant and the order of a Lipschitz continuous function. We are also concerned with the monotonicity of a sequence of such operators for convex functions.

Publisher

Academia Romana Filiala Cluj

Reference15 articles.

1. U. Abel and M. Ivan, On a generalization of an approximation operator defined by A. Lupaş, Gen. Math., 15 (2007) no. 1, pp. 21-34.

2. T. Acar and A. Aral, Approximation properties of two dimensional Bernstein-Stancu-Chlodowsky operators, Matematiche (Catania), 68 (2013) no. 2, pp. 15-31, http://dx.doi.org/10.4418/2013.68.2.2

3. O. Agratini, On a sequence of linear positive operators, Facta Univ. Ser. Math. Inform., 14 (1999), pp. 41-48.

4. B. M. Brown, D. Elliott and D.F. Paget, Lipschitz constants for the Bernstein polynomials of a Lipschitz continuous function, J. Approx. Theory, 49 (1987) no. 2, pp. 196-199, http://dx.doi.org/10.1016/0021-9045(87)90087-6

5. F. Dirik, Statistical convergence and rate of convergence of a sequence of positive linear operators, Math. Commun., 12 (2007) no. 2, pp. 147-153.

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