General Summability Methods in the Approximation by Bernstein–Chlodovsky Operators
Meryem Ece Alemdar, Oktay Duman
Abstract
In this paper, by using regular summability methods we modify the Bernstein–Chlodovsky operators in order get more general and powerful results than the classical aspects. We study Korovkin-type approximation theory on weighted spaces. As a special case, it is possible to Cesàro approximate (arithmetic mean convergence) to the test function e2(x)=x2 although it fails for the classical Bernstein–Chlodovsky operators. At the end of the paper, we extend our results to the multi-dimensional case.
Topics & Concepts
MathematicsBernstein polynomialConvergence (economics)Operator theoryBaskakov operatorOrder (exchange)Type (biology)Linear operatorsFunction (biology)Applied mathematicsPure mathematicsAlgebra over a fieldMathematical analysisMicrolocal analysisFourier integral operatorEconomicsFinanceEvolutionary biologyBiologyBounded functionEconomic growthEcologyApproximation Theory and Sequence SpacesMathematical Approximation and IntegrationIterative Methods for Nonlinear Equations