Szász-Baskakov type operators based on q -integers

Journal of inequalities and applications

Purshottam N Agrawal¹ 

关键词: Szász-Baskakov operators;    rate of convergence;    modulus of continuity;    weighted approximation;    point-wise estimates;    Lipschitz type maximal function;    statistical convergence;   

DOI  :  10.1186/1029-242X-2014-441

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In the present paper, we introduce the q-analog of the Stancu variant of Szász-Baskakov operators. We establish the moments of the operators by using the q-derivatives and then prove the basic convergence theorem. Next, the Voronovskaja type theorem and some direct results for the above operators are discussed. Also, the rate of convergence and weighted approximation by these operators in terms of modulus of continuity are studied. Then we obtain a point-wise estimate using the Lipschitz type maximal function. Lastly, we study the A-statistical convergence of these operators and also, in order to obtain a better approximation, we study a King type modification of the above operators. MSC:41A25, 26A15, 40A35.

【 授权许可】

CC BY