Local Approximation Properties for the New Type q-Stancu-Durrmeyer Operators

Author:

SABANCIGİL ÖZDER Pembe1

Affiliation:

1. DOĞU AKDENİZ ÜNİVERSİTESİ

Abstract

In this article, we propose a new kind of q-Stancu-Durrmeyer operators (or shortly q-SD operators). We calculate first and second order moments, for and we give an estimation for the second order central moment, . Furthermore, through the use of the second modulus of continuity, we invent approximation properties of the q-SD operators in the local sense and by using order Lipschitz kind maximal function, we give a direct estimation for the q-SD operators again in the local sense.

Publisher

Osmaniye Korkut Ata Universitesi

Subject

General Agricultural and Biological Sciences

Reference10 articles.

1. Büyükyazıcı İ. Approximation by Stancu-Chlodowsky polynomials. Comput. and Math. with Appl., 2010; 59(1): 274-282.

2. Büyükyazıcı İ. Direct and converse theorems for generalized Bernstein polynomials based on qintegers. J. App. Func. Anal., 2012; 7(1/2): 81-97.

3. Büyükyazıcı İ., Sharma H. Approximation properties of two dimensional q-Bernstein-Chlodowsky- Durrmeyer operators. Numer. Func. Anal. and Opt., 2012; (12): 1351-1371.

4. Ditzian Z., Totik V. Moduli of smoothness, Springer Verlag, New York, 1987.

5. Durrmeyer JL. Une formule d inversion de la transformee laplace, applications a la theorie des moments. These de 3e cycle, Faculte des Sciences de I Universite de Paris, 1967.

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