Mathematica Bohemica, first online, pp. 16, 2017


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

Mohammad Mursaleen, Ahmed A. H. Alabied

Received October 8, 2016.  First published June 20, 2017.

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 ${\rm Lip}_M(\gamma)$.
Keywords:  $(p, q)$-integer; $(p, q)$-Bernstein-Durrmeyer operator; $q$-Bernstein-Durrmeyer operator; modulus of continuity; positive linear operator; Korovkin type approximation theorem
Classification MSC:  41A10, 41A25, 41A36
DOI:  10.21136/MB.2017.0086-16

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Affiliations:   Mohammad Mursaleen, Ahmed A. H. Alabied, Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India, e-mail: mursaleenm@gmail.com, abied1979@gmail.com


 
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