On statistical approximation properties of q -Baskakov–Szász–Stancu operators

Mishra, Vishnu Narayan; Sharma, Preeti; Mishra, Lakshmi Narayan

doi:10.1016/j.joems.2015.07.005

On statistical approximation properties of q -Baskakov–Szász–Stancu operators

Authors

¹ Department of Applied Mathematics & Humanities, Sardar Vallabhbhai National Institute of Technology, Ichchhanath Mahadev Dumas Road, Surat 395 007, Gujarat, India

² L.1627 Awadh Puri Colony Beniganj, Phase-III, Opposite Industrial Training Institute (I.T.I.), Ayodhya Main Road, Faizabad 224 001, Uttar Pradesh, India

³ Department of Mathematics, National Institute of Technology, Silchar 788 010, Cachar, Assam, India

10.1016/j.joems.2015.07.005

Abstract

In the present paper, we consider Stancu type generalization of Baskakov–Szász opera-
tors based on the q -integers and obtain statistical and weighted statistical approximation properties
of these operators. Rates of statistical convergence by means of the modulus of continuity and the
Lipschitz type maximal function are also established for operators.

Keywords