Certain approximation properties of Brenke polynomials using Jakimovski–Leviatan operators
Shahid Ahmad Wani, M. Mursaleen, Kottakkaran Sooppy Nisar
Abstract
Abstract In this article, we establish the approximation by Durrmeyer type Jakimovski–Leviatan operators involving the Brenke type polynomials. The positive linear operators are constructed for the Brenke polynomials, and thus approximation properties for these polynomials are obtained. The order of convergence and the weighted approximation are also considered. Finally, the Voronovskaya type theorem is demonstrated for some particular case of these polynomials.
Topics & Concepts
MathematicsClassical orthogonal polynomialsBaskakov operatorOrthogonal polynomialsDiscrete orthogonal polynomialsDifference polynomialsEquioscillation theoremWilson polynomialsType (biology)Jacobi polynomialsConvergence (economics)Gegenbauer polynomialsOrder (exchange)Hahn polynomialsPure mathematicsOperator theoryApplied mathematicsFourier integral operatorMicrolocal analysisEconomic growthEconomicsBiologyEcologyFinanceApproximation Theory and Sequence SpacesIterative Methods for Nonlinear EquationsMathematical Approximation and Integration