Approximation by bivariate generalized Bernstein–Schurer operators and associated GBS operators
S. A. Mohiuddine
Abstract
Abstract We construct the bivariate form of Bernstein–Schurer operators based on parameter α . We establish the Voronovskaja-type theorem and give an estimate of the order of approximation with the help of Peetre’s K -functional of our newly defined operators. Moreover, we define the associated generalized Boolean sum (shortly, GBS) operators and estimate the rate of convergence by means of mixed modulus of smoothness. Finally, the order of approximation for Bögel differentiable function of our GBS operators is presented.
Topics & Concepts
MathematicsBivariate analysisModulus of continuityOperator theoryOrdinary differential equationSmoothnessSpectral theoremOrder (exchange)Differentiable functionFourier integral operatorApplied mathematicsMicrolocal analysisType (biology)Constant coefficientsRate of convergencePure mathematicsMathematical analysisDifferential equationStatisticsEcologyElectrical engineeringFinanceEconomicsEngineeringBiologyChannel (broadcasting)Approximation Theory and Sequence SpacesIterative Methods for Nonlinear EquationsMathematical Inequalities and Applications