ANNALI DELL'UNIVERSITA' DI FERRARA

, Volume 63, Issue 2, pp 289–302

# Bézier variant of the Jakimovski–Leviatan–Păltănea operators based on Appell polynomials

Article

## Abstract

In this paper, we introduce the Bézier variant of the Jakimovski–Leviatan–Păltănea operators based on Appell polynomials. We establish some local results, a direct approximation theorem by means of the Ditzian–Totik modulus of smoothness and also study the rate of convergence for the functions having a derivative of bounded variation for these operators.

### Keywords

Bézier operator Modulus of continuity Rate of convergence Bounded variation

### Mathematics Subject Classification

26A15 40A35 41A25 41A36

## Notes

### Acknowledgements

The authors are extremely grateful to the reviewers for a careful reading of the manuscript and making helpful suggestions leading to a better presentation of the paper. The first author is thankful to the “Council of Scientific and Industrial Research” India for financial support to carry out the above research work.

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