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RESEARCH PRODUCT

Some approximation properties of ( p , q ) $(p,q)$ -Bernstein operators

Arif RafiqFaisal AliYoung Chel KwunShin Min KangAna Maria Acu

subject

MapleDiscrete mathematicsModulus of smoothnesslcsh:MathematicsApplied Mathematics010102 general mathematicsApproximation theoremRegular polygonMonotonic functionFunction (mathematics)Type (model theory)engineering.materialVoronovskaja type theoremlcsh:QA1-93901 natural sciences010101 applied mathematics( p q ) $(pq)$ -Bernstein operatorsengineeringDiscrete Mathematics and Combinatorics0101 mathematics( p q ) $(pq)$ -calculusK-functionalAnalysisMathematicsDitzian-Totik first order modulus of smoothness

description

This paper is concerned with the $(p,q)$ -analog of Bernstein operators. It is proved that, when the function is convex, the $(p,q)$ -Bernstein operators are monotonic decreasing, as in the classical case. Also, some numerical examples based on Maple algorithms that verify these properties are considered. A global approximation theorem by means of the Ditzian-Totik modulus of smoothness and a Voronovskaja type theorem are proved.

yearjournalcountryeditionlanguage
2016-06-01Journal of Inequalities and Applications
10.1186/s13660-016-1111-3http://dx.doi.org/10.1186/s13660-016-1111-3