10.1186/2251-7456-6-26

A certain family of mixed summation-integral-type Lupaş-Phillips-Bernstein operators

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  • Honey Sharma*1,
  • Jaspal Singh Aujla1,
  1. Department of Mathematics, National Institute of Technology, Jalandhar, Punjab, 144011, IN
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Published in Issue 2012-08-17

How to Cite

Sharma, H., & Aujla, J. S. (2012). A certain family of mixed summation-integral-type Lupaş-Phillips-Bernstein operators. Mathematical Sciences, 6(1). https://doi.org/10.1186/2251-7456-6-26
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Abstract

Abstract Purpose The purpose of this paper is to introduce the mixed summation-integral-type Lupaş-Phillips-Bernstein operators. Methods Firstly, we compute the moments of the operators. We use the method of Korovkin-type statistical approximation and modulus of continuity. Results We find the rate of convergence of the modified operators using statistical convergence and modulus of continuity. Conclusions The rate of convergence of the modified mixed operators is sufficiently sharp.

Keywords

  • q-integers,
  • q-integration,
  • Lupaş operator,
  • q-Bernstein operator,
  • Statistical convergence,
  • Modulus of continuity,
  • Mathematical subject classification 41A25; S 41A35
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