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Approximation for link Ismail–May operators

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Abstract

In the present paper, we discuss the approximation properties of certain link integral modification of Ismail–May operators. We point out here that the operators of Ismail–May can also be derived from the Jain operators. We also establish some direct convergence estimates including error, difference estimates and an asymptotic formula in simultaneous approximation. In the end, we indicate through graphical representation the convergence of polynomial function with the link operators.

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Acknowledgements

The authors are extremely thankful to the reviewers for their valuable suggestions, leading to overall improvements in the manuscript.

Author information

Correspondence to Vijay Gupta.

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The authors declare that they have no conflict of interest.

Additional information

Communicated by Gradimir Milovanovic.

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Gupta, V., Agrawal, G. Approximation for link Ismail–May operators. Ann. Funct. Anal. (2020) doi:10.1007/s43034-019-00051-y

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Keywords

  • Ismail–May operators
  • Jain operators
  • Convergence estimates
  • Difference estimates
  • Simultaneous approximation

Mathematics Subject Classification

  • 41A25
  • 41A30