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arXiv · 2212.05305

Iterative Roots of Multifunctions

B. V. Rajarama Bhat·Chaitanya Gopalakrishna
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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 has been illustrated by showing the nonexistence of iterative roots of some specified orders for certain complex polynomials.

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BibTeXRIS

B. V. Rajarama Bhat, Chaitanya Gopalakrishna. 2022-12-10. Iterative Roots of Multifunctions. https://arxiv.org/abs/2212.05305

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