Chlodowsky variant of q -Bernstein-Schurer-Stancu operators

Journal of inequalities and applications

Tuba Vedi¹ 

关键词: Schurer-Stancu and Schurer Chlodowsky operators;    modulus of continuity;    Korovkin-type theorems;    Lipschitz-type functionals;    q-Bernstein operators;   

DOI  :  10.1186/1029-242X-2014-189

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

It was Chlodowsky who considered non-trivial Bernstein operators, which help to approximate bounded continuous functions on the unbounded domain. In this paper, we introduce the Chlodowsky variant of q-Bernstein-Schurer-Stancu operators. By obtaining the first few moments of these operators, we prove Korovkin-type approximation theorems in different function spaces. Furthermore, we compute the error of the approximation by using the modulus of continuity and Lipschitz-type functionals. Then we obtain the degree of the approximation in terms of the modulus of continuity of the derivative of the function. Finally, we study the generalization of the Chlodowsky variant of q-Bernstein-Schurer-Stancu operators and investigate their approximations. MSC:41A10, 41A25, 41A36.

【 授权许可】

CC BY