The approximation operators provided by classical approximation theory use exclusively as underlying algebraic structure the linear structure of the reals. Also they are all linear operators. We address in the present paper the following problems: Need all the approximation operators be linear? Is the linear structure the only one which allows us to construct particular approximation operators? As an answer to this problem we propose new, particular, pseudo-linear approximation operators, which are defined in some ordered semirings. We study these approximations from a theoretical point of view and we obtain that these operators have very similar properties to those provided by classical approximation theory. In this sense we obtain uniform approximation theorems of Weierstrass type, and Jackson-type error estimates in approximation by these operators.
Approximation by pseudo-linear operators
DI NOLA, Antonio
2008-01-01
Abstract
The approximation operators provided by classical approximation theory use exclusively as underlying algebraic structure the linear structure of the reals. Also they are all linear operators. We address in the present paper the following problems: Need all the approximation operators be linear? Is the linear structure the only one which allows us to construct particular approximation operators? As an answer to this problem we propose new, particular, pseudo-linear approximation operators, which are defined in some ordered semirings. We study these approximations from a theoretical point of view and we obtain that these operators have very similar properties to those provided by classical approximation theory. In this sense we obtain uniform approximation theorems of Weierstrass type, and Jackson-type error estimates in approximation by these operators.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
