Statistical approximation by Kantorovich-type discrete q -Betaoperators

Advances in Difference Equations

Kejal Khatri¹  Vishnu Narayan Mishra¹  Lakshmi Narayan Mishra² 

[1] Applied Mathematics and Humanities Department, Sardar Vallabhbhai National Institute of Technology, Surat, India;L. 1627 Awadh Puri Colony Beniganj, Faizabad, India

关键词: discrete q-Beta operators;    Kantorovich-type operators;    Korovkin-type approximation theorem;    rate of statistical convergence;    modulus of continuity;    Lipschitz-type functions;   

DOI  :  10.1186/1687-1847-2013-345

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The aim of the present paper is to introduce a Kantorovich-type modification ofthe q-discrete beta operators and to investigate their statistical andweighted statistical approximation properties. Rates of statistical convergenceby means of the modulus of continuity and the Lipschitz-type function are alsoestablished for operators. Finally, we construct a bivariate generalization ofthe operator and also obtain the statistical approximation properties. MSC: 41A25, 41A36.

【 授权许可】

CC BY