5 papers · 1 filter
A new class of positive linear operators preserving logarithmic functions
Laura Angeloni, Danilo Costarelli, Chiara Darielli
In this paper, we introduce a new class of positive linear operators that generalize the classical Bernstein operators. Specifically, we construct a sequence of operators that repr…
A Kantorovich version of Bernstein-type logarithmic operators
Laura Angeloni, Danilo Costarelli, Chiara Darielli
In this paper, we introduce a Kantorovich version of the Bernstein-type logarithmic operators. The idea comes from the wide literature concerning exponential polynomials that prese…
Strong and weak sharp bounds for Neural Network Operators in Sobolev-Orlicz spaces and their quantitative extensions to Orlicz spaces
Danilo Costarelli, Michele Piconi
In this paper, we establish sharp bounds for a family of Kantorovich-type neural network operators within the general frameworks of Sobolev-Orlicz and Orlicz spaces. We establish b…
Saturation theorems for neural network operators by solving elliptic and hyperbolic PDEs with analytical and semi-analytical inverse problems
Danilo Costarelli
This paper addresses inverse problems (in a broad sense) for two classes of multivariate neural network (NN) operators, with particular emphasis on saturation results, and both ana…
Modular convergence of Steklov sampling operators in Orlicz spaces
Danilo Costarelli, Erika Russo
In this paper, we deal with the family of Steklov sampling operators in the general setting of Orlicz spaces. The main result of the paper is a modular convergence theorem establis…