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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Degree of Approximation by Certain Durrmeyer Type Operators

Discontinuity, Nonlinearity, and Complexity 11(2) (2022) 253--273 | DOI:10.5890/DNC.2022.06.006

Asha Ram Gairola$^1$, Karunesh Kumar Singh$^2$, Lakshmi Narayan Mishra$^3$

$^1$ Department of Mathematics, Doon University, Dehradun-248001 (Uttarakhand), India

$^2$ Department of Applied Sciences and Humanities Institute of Engineering and Technology Lucknow-226021

(Uttar Pradesh), India

$^3$ Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (VIT) University,

Vellore 632 014, Tamil Nadu, India

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We obtain local and global rate of approximation by two new variants, $D_n^{M,1}(f,x)$ and $D_n^{M,2}(f,x)$ of Bernstein Durrmeyer operators, recently introduced by Acu et al. By utilizing a suitable Ditzian-Totik modulus of smoothness, we prove that the approximation process $D_n^{M,2}(f,x)$ is quadratic convergent. An error estimate for the functions of bounded variation by the B\'{e}zier variant of the operators $D_n^{M,1}(f,x)$ is obtained.


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