0000000000594473

AUTHOR

Shin Min Kang

showing 2 related works from this author

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

2016

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.

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 smoothnessJournal of Inequalities and Applications
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Approximation properties of q-Kantorovich-Stancu operator

2015

In this paper we study some properties of Kantorovich-type generalizations of the q-Stancu operators. We obtain some approximation properties for these operators, estimating the rate of convergence by using the first and second modulus of continuity. Also, we investigate the statistical approximation properties of the q-Kantorovich-Stancu operators using the Korovkin-type statistical approximation theorem.

Operator (computer programming)Rate of convergenceStatistical approximationApplied MathematicsMathematical analysisDiscrete Mathematics and CombinatoricsSpouge's approximationSpectral theoremOperator theoryOperator normAnalysisModulus of continuityMathematicsJournal of Inequalities and Applications
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