MMN-2145

# On computable classes of equidistant sets: equidistant functions

**Cs. Vincze**, University of Debrecen, Institute of Mathematics, H-4002 Debrecen, P.O.Box 400, Debrecen, Hungary,`csvincze@science.unideb.hu`

**A. Varga**, University of Debrecen, Faculty of Engineering, H-4002 Debrecen, P.O.Box 400, Debrecen, Hungary,`vargaa@eng.unideb.hu`

**M. Oláh**, University of Debrecen, BSC mathematics, H-4002 Debrecen, P.O.Box 400, Debrecen, Hungary,`olma4000@euromail.hu`

**L. Flórián**, University of Debrecen, BSC mathematics, H-4002 Debrecen, P.O.Box 400, Debrecen, Hungary,`laci.forian@gmail.com`

## Abstract

In their paper \cite{PS} the authors posed the problem of the characterization of closed subsets in the Euclidean plane that can be realized as the equidistant set of two connected disjoint closed sets. We are going to solve the problem for a special class of equidistant sets. As a main result we give necessary and sufficient conditions for a function to be a so-called equidistant function. This means that its graph is the equidistant set of a line (the first coordinate axis) and the (convex) epigraph of a positive valued convex function satisfying some regularity conditions.

Vol. 19 (2018), No. 1, pp. 677-689

DOI: 10.18514/MMN.2018.2145