tailieunhanh - Báo cáo hóa học: "Research Article q-Parametric Bleimann Butzer and Hahn Operators"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article q-Parametric Bleimann Butzer and Hahn Operators | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 816367 15 pages doi 2008 816367 Research Article q-Parametric Bleimann Butzer and Hahn Operators N. I. Mahmudov and P. Sabancigil Eastern Mediterranean University Gazimagusa Turkish Republic of Northern Cyprus Mersin 10 Turkey Correspondence should be addressed to N. I. Mahmudov Received 4 June 2008 Accepted 20 August 2008 Recommended by Vijay Gupta We introduce a new q-parametric generalization of Bleimann Butzer and Hahn operators in C 1V 0 to . We study some properties of q-BBH operators and establish the rate of convergence for q-BBH operators. We discuss Voronovskaja-type theorem and saturation of convergence for q-BBH operators for arbitrary fixed 0 q 1. We give explicit formulas of Voronovskaja-type for the q-BBH operators for 0 q 1. Also we study convergence of the derivative of q-BBH operators. Copyright 2008 N. I. Mahmudov and P. Sabancigil. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction q-Bernstein polynomials Bn q f x ịf k 0 n n k n-k-1 xk n 1 - qX s 0 were introduced by Phillips in 1 . q-Bernstein polynomials form an area of an intensive research in the approximation theory see survey paper 2 and references therein. Nowadays there are new studies on the q-parametric operators. Two parametric generalizations of q-Bernstein polynomials have been considered by Lewanowicz and WoZny cf. 3 an analog of the Bernstein-Durrmeyer operator and Bernstein-Chlodowsky operator related to the q-Bernstein basis has been studied by Derriennic 4 Gupta 5 and Karsli and Gupta 6 respectively a q-version of the Szasz-Mirakjan operator has been investigated by Aral and Gupta in 7 . Also some results on q-parametric Meyer-Konig and Zeller operators can be found in 8-11