Approximation by Composition of q-SZASZ-Mirayan and q-Durrmeyer-Chlodowsky Operators

Year 2017, Volume: 7, 83 - 89, 19.12.2017

Aydın İzgi , Ecem Acar

Abstract

In the present paper, we introduce q-Sz´asz Mirakyan operators by taking the weight function of q-Chlodowsky-Durrmeyer operators on C[0;1) and investigate their approximation properties. We give weighted approximation theorem.

Keywords

Approximation, Szˆasz-Mirakyan Operators, Chlodowsky-Durrmeyer Operators, Voronovskaya type theorem.

References

• Büyükyazıcı, I., Tanberkan, H., Kırcı Serenbay, S., Atakut, Ç., Approximation by Chlodowsky type Jakimovskiy Leviatan operators, Journal of Computational and Applied Mathematics, 259(2013), 153--163.
• Dalmanoglu, Ö., Kırcı Serenbay, S., Approximation by Chlodowsky type q-Jakimovski-Leviatan operators, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 65(1)(2016), 157--169.
• Gupta, V., Heping, W., The rate of convergence of q-Durrmeyer operators for $0< q <1$, Math. Methods Appl. Sci., 31(2008), 1946--1955.
• Ispir, N., On modified Baskakov operators on weighted spaces, Turk. J. Math., 26(2001), 355--365.
• İzgi, A., Approximation by composition of Szasz-Mirakyan and Durrmeyer-Chlodowsky operators}, Eurasian Mathematical Journel ISSN 2077-9879, 3(1)(2012), 63--71.
• Kac, V., Cheung, P., Quantum Calculus, Universitext, Springer-Verlag, New York, 2002.
• Mahmudov, N.I., Kaffaoğlu, H., On $q$-Szasz-Durrmeyer operators, Central European Journal of Mathematics, 8(2010),399--409.
• Phillips, G.M., Bernstein polynominals based on the q-integers, Ann. Number. Math., 4(1997), 511--518.