Genuine modified Bernstein–Durrmeyer operators

Abstract

Abstract The present paper deals with genuine Bernstein–Durrmeyer operators which preserve some certain functions. The rate of convergence of new operators via a Peetre K $\mathcal{K}$-functional and corresponding modulus of smoothness, quantitative Voronovskaya type theorem and Grüss–Voronovskaya type theorem in quantitative mean are discussed. Finally, the graphic for new operators with special cases and for some values of n is also presented.

Keywords

• Genuine Bernstein–Durrmeyer operators
• Rate of convergence
• Quantitative Voronovskaya theorem
• Gruss–Voronovskaya theorem