Convergence Properties of Certain Positive Linear Operators

Acu A., Manav N., Ratiu A.

RESULTS IN MATHEMATICS, cilt.74, sa.1, 2019 (SCI İndekslerine Giren Dergi) identifier identifier


The present paper deals with the modified positive linear operators that present a better degree of approximation than the original ones. This new construction of operators depend on a certain function defined on [0, 1]. Some approximation properties of these operators are given. Using the first order Ditzian-Totik modulus of smoothness, some Voronovskaja type theorems in quantitative mean are proved. The main results proved in this paper are applied for Bernstein operators, Lupas operators and genuine Bernstein-Durrmeyer operators. By numerical examples we show that depending on the choice of the function , the modified operator presents a better order of approximation than the classical ones.