Bivariate Bernstein polynomials that reproduce exponential functions
Kenan BOZKURT, Fırat Özsaraç, Ali̇ Aral
2021Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics14 citationsDOIOpen Access PDF
Abstract
In this paper, we construct Bernstein type operators that reproduce exponential functions on simplex with one moved curved side. The operator interpolates the function at the corner points of the simplex. Used function sequence with parameters and not only are gained more modeling exibility to operator but also satised to preserve some exponential functions. We examine the convergence properties of the new approximation processes. Later, we also state its shape preserving properties by considering classical convexity. Finally, a Voronovskaya-type theorem is given and our results are supported by graphics.
Topics & Concepts
Operator (biology)MathematicsBivariate analysisSimplexExponential functionConvexityExponential typeSequence (biology)Applied mathematicsConvergence (economics)Exponential formulaBernstein polynomialFunction (biology)Type (biology)Mathematical analysisPure mathematicsCombinatoricsDouble exponential functionStatisticsGeneticsEconomicsEconomic growthGeneEcologyRepressorBiologyFinancial economicsChemistryEvolutionary biologyBiochemistryTranscription factorApproximation Theory and Sequence SpacesAdvanced Numerical Analysis TechniquesIterative Methods for Nonlinear Equations