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Compatibility Conditions for Systems of Iterative Functional Equations with Non-trivial Contact Sets

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Abstract

Systems of iterative functional equations with a non-trivial set of contact points are not necessarily solvable, as the resulting intersections may lead to an overdetermination of the system. To obtain existence and uniqueness results additional conditions must be imposed on the system. These are the compatibility conditions, which we define and study in a general setting. An application to the affine and doubly affine cases allows us to solve an open problem in the theory of functional equations. In the last section we consider a special problem in a different perspective, showing that a complex compatibility condition may result in an elegant and simple property of the solution.

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Acknowledgements

The authors acknowledge fruitful discussions with Prof. Pedro Duarte and partial support by National Funding from FCT - Fundação para a Ciência e a Tecnologia, under the project: UIDB/04561/2020.

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Partial support by National Funding from FCT - Fundação para a Ciência e a Tecnologia, under the project: UIDB/04561/2020

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Lead author: Cristina Serpa.

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Correspondence to Cristina Serpa.

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Partial support by National Funding from FCT - Fundação para a Ciência e a Tecnologia, under the project: UIDB/04561/2020.

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Buescu, J., Serpa, C. Compatibility Conditions for Systems of Iterative Functional Equations with Non-trivial Contact Sets. Results Math 76, 68 (2021). https://doi.org/10.1007/s00025-021-01365-x

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