## Iterative roots of multifunctions

Fundamenta Mathematicae
MSC: Primary 39B12; Secondary 54C60, 05C20
DOI: 10.4064/fm299-12-2023
Published online: 16 February 2024

#### Abstract

Some easily verifiable sufficient conditions for the nonexistence of iterative roots for multifunctions on arbitrary nonempty sets are presented. Typically if the graph of the multifunction has a distinguished point with a relatively large number of paths leading to it then such a multifunction does not admit any iterative root. These results can be applied to single-valued maps by considering their pullbacks as multifunctions. This is illustrated by showing the nonexistence of iterative roots of some specified orders for certain complex polynomials.