Approximation properties for modified ( p , q ) -Bernstein-Durrmeyer operators

Mohammad Mursaleen; Ahmed A. H. Alabied

Mathematica Bohemica (2018)

  • Volume: 143, Issue: 2, page 173-188
  • ISSN: 0862-7959

Abstract

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We introduce modified ( p , q ) -Bernstein-Durrmeyer operators. We discuss approximation properties for these operators based on Korovkin type approximation theorem and compute the order of convergence using usual modulus of continuity. We also study the local approximation property of the sequence of positive linear operators D n , p , q * and compute the rate of convergence for the function f belonging to the class Lip M ( γ ) .

How to cite

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Mursaleen, Mohammad, and Alabied, Ahmed A. H.. "Approximation properties for modified $(p,q)$-Bernstein-Durrmeyer operators." Mathematica Bohemica 143.2 (2018): 173-188. <http://eudml.org/doc/294575>.

@article{Mursaleen2018,
abstract = {We introduce modified $(p,q)$-Bernstein-Durrmeyer operators. We discuss approximation properties for these operators based on Korovkin type approximation theorem and compute the order of convergence using usual modulus of continuity. We also study the local approximation property of the sequence of positive linear operators $\{D\}_\{n,p,q\}^\{\ast \}$ and compute the rate of convergence for the function $f$ belonging to the class $\{\rm Lip\}_\{M\}(\gamma )$.},
author = {Mursaleen, Mohammad, Alabied, Ahmed A. H.},
journal = {Mathematica Bohemica},
keywords = {$(p, q)$-integer; $(p, q)$-Bernstein-Durrmeyer operator; $q$-Bernstein-Durrmeyer operator; modulus of continuity; positive linear operator; Korovkin type approximation theorem},
language = {eng},
number = {2},
pages = {173-188},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Approximation properties for modified $(p,q)$-Bernstein-Durrmeyer operators},
url = {http://eudml.org/doc/294575},
volume = {143},
year = {2018},
}

TY - JOUR
AU - Mursaleen, Mohammad
AU - Alabied, Ahmed A. H.
TI - Approximation properties for modified $(p,q)$-Bernstein-Durrmeyer operators
JO - Mathematica Bohemica
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 143
IS - 2
SP - 173
EP - 188
AB - We introduce modified $(p,q)$-Bernstein-Durrmeyer operators. We discuss approximation properties for these operators based on Korovkin type approximation theorem and compute the order of convergence using usual modulus of continuity. We also study the local approximation property of the sequence of positive linear operators ${D}_{n,p,q}^{\ast }$ and compute the rate of convergence for the function $f$ belonging to the class ${\rm Lip}_{M}(\gamma )$.
LA - eng
KW - $(p, q)$-integer; $(p, q)$-Bernstein-Durrmeyer operator; $q$-Bernstein-Durrmeyer operator; modulus of continuity; positive linear operator; Korovkin type approximation theorem
UR - http://eudml.org/doc/294575
ER -

References

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