#### Conference abstracts

Session A1 - Approximation Theory

July 12, 17:40 ~ 18:15 - Room B3

## Approximation of set-valued functions by adaptation of classical approximation operators to sets

### Nira Dyn

### School of Mathematical Sciences, Tel-Aviv University, Israel - niradyn@post.tau.ac.il

In this talk we consider approximation of univariate set-valued functions, mapping a closed interval to compact sets in a Euclidean space. Since the collection of such sets is not a vector space, the classical approximation operators have to be adapted to this setting. One way is to replace operations between numbers, by operations between sets. When the approximation error is measured in the Hausdorff metric, the operations between sets, designed by us, lead to error bounds expressed in terms of the regularity properties of the approxinated set-valued function.

An example of a possible application of the theory to the approximation of a 3D object from its parallel 2D cross-sections concludes the talk.

Joint work with Elza Farkhi (Tel-Aviv University, Israel) and Alona Mokhov (Afeka College, Tel-Aviv, Israel).