Wyniki wyszukiwania - BazTech

1

Order of approximation for nonlinear sampling Kantorovich operators in Orlicz spaces

Costarelli D., Vinti G.

Commentationes Mathematicae

|

2013

|

Vol. 53, No. 2

171--192

EN

In this paper, we study the rate of approximation for the nonlinear sampling Kantorovich operators. We consider the case of uniformly continuous and bounded functions belonging to Lipschitz classes of the Zygmund-type, as well as the case of functions in Orlicz spaces. We estimate the aliasing errors with respect to the uniform norm and to the modular functional of the Orlicz spaces, respectively. The general setting of Orlicz spaces allows to deduce directly the results concerning the rate of convergence in Lp-spaces, 1 ≤ p < ∞, very useful in the applications to Signal Processing. Others examples of Orlicz spaces as interpolation spaces and exponential spaces are discussed and the particular cases of the nonlinear sampling Kantorovich series constructed using Fejér and B-spline kernels are also considered.

2

On the order of BVφ - approximation of convolution integrals over the line group

Bardaro C., Vinti G.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

|

2004

|

Vol. 44, nr spec.

47-63

EN

Here we study the rate of BVφ - approximation of higher order for a class of linear integral operators of convolution type over the line group.

3

On nonlinear integral equations in some functions spaces

Bardaro C., Musielak J., Vinti G.

Demonstratio Mathematica

|

2002

|

Vol. 35, nr 3

583-592

EN

There are established some conditions for existence of solutions of a nonlinear integral equation Tf =f+g, where T is a convolution-type integral operator.

4

Urysohn integral operators with homogeneous kernel : approximation properties in modular spaces

Bardaro C., Vinti G.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

|

2002

|

[Z] 42(2)

145-182

EN

Here we state some modular approximation theorems for a class of nonlinear integral operators, acting on functions defined on locally compact groups, whose kernels satisfy some Lipschitz conditions and some general homogeneity assumptions. Moreover we study the order of modular approximation in modular Lipschitz classes. Applications to nonlinear Mellin convolution operators are given.