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Study of Sensitivity of Parameters of Bernstein–Stancu Operators

  • Vishnu Narayan MishraEmail author
  • R. B. Gandhi
Research Paper
  • 29 Downloads
Part of the following topical collections:
  1. Mathematics

Abstract

This paper is aimed at studying sensitivity of parameters \(\alpha \) and \(\beta \) appearing in the operators introduced by Stancu (Studia Universitatis Babes-Bolyai 14(2):31–45, 1969). Results are established on the behavior of the nodes used in Bernstein–Stancu polynomials and the nodes used in Bernstein polynomials and graphical presentations of them are generated. Alternate proof of uniform convergence of Bernstein–Stancu operators and an upper bound estimation are derived. It is also established that the parameters \(\alpha \) and \(\beta \) in Bernstein–Stancu polynomials can be used to get better approximation at a point \(x = \alpha /\beta \) in [0, 1] to the Bernstein polynomials.

Keywords

Bernstein operators Bernstein–Stancu operators 

Mathematics Subject Classification

41A10 41A36 

Notes

Acknowledgements

The authors are thankful to Rodin Lusan and Barbara Strazzabosco of Zentralblatt MATH, Berlin, Germany, who took all the trouble to manage us the paper (Stancu 1969) from Studia UBB, Romania. The authors are thankful to the reviewers for making valuable suggestions leading to a better presentation of the paper.

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Copyright information

© Shiraz University 2019

Authors and Affiliations

  1. 1.Department of MathematicsIndira Gandhi National Tribal UniversityAmarkantakIndia
  2. 2.Department of MathematicsBVM Engineering CollegeVallabh VidyanagarIndia
  3. 3.AyodhyaIndia

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