Indian Journal of Industrial and Applied Mathematics
  • Year: 2019
  • Volume: 10
  • Issue: 1SI

On a Class of Generalised (p, q) Bernstein Operators

  • Author:
  • Lakshmi Narayan Mishra1,, Shikha Pandey2,, Vishnu Narayan Mishra3,
  • Total Page Count: 4
  • Published Online: Jun 1, 2019
  • Page Number: 220 to 223

1Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (VIT) University, Vellore-632014, Tamil Nadu, India

2Department of Applied Mathematics & Humanities, Sardar Vallabhbhai National Institute of Technology, Ichchhanath Mahadev Dumas Road, Surat-395 007 (Gujarat), India

3Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak-484 887, Madhya Pradesh, India

(*Corresponding author) Email: *lakshminarayanmishra04@gmail.com

**sp1486@gmail.com

***vishnunarayanmishra@gmail.com

Abstract

In the present paper, we introduce a generalised class of (p, q) Bernstein operators. The study proves that this generalised operator gives better approximation results comparison to the (p, q) Bernstein operators defined in [11]. We estimate the rate of approximation using modulus of continuity and prove Voronovskaya type theorem as well. In the end we have proved the statistical and weighted approximation results for this operator.

Keywords

(p, q)-integers, (p, q)-Bernstein operators, modulus of continuity, linear positive operators, Primary 41A25, 41A36