Abstract
We construct the Stancu-type generalization of q-Bernstein operators involving the idea of Bézier bases depending on the shape parameter −1≤ζ≤1 and obtain auxiliary lemmas. We discuss the local approximation results in term of a Lipschitz-type function based on two parameters and a Lipschitz-type maximal function, as well as other related results for our newly constructed operators. Moreover, we determine the rate of convergence of our operators by means of Peetre’s K-functional and corresponding modulus of continuity.
Funder
National Natural Science Foundation of China
Key Natural Science Research Project in Universities of Anhui Province
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference38 articles.
1. Démonstration du théoréme de Weierstrass fondée sur le calcul des probabilités;Bernstein;Commun. Soc. Math. Kharkow,1913
2. A q-analogue of the Bernstein operator;Lupaş,1987
3. Bernstein polynomials based on the q-integers;Phillips;Ann. Numer. Math.,1997
4. The rate of convergence of q-Bernstein polynomials for 0;Heping;J. Approx. Theor.,2005
5. On the rates of convergence of the q-Lupaş-Stancu operators
Cited by
7 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献