Compatibility conditions for systems of iterative functional equations with non-trivial contact sets
| Autor: | Jorge Buescu, Cristina Serpa |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Contact set
Property (philosophy) Applied Mathematics Open problem 010102 general mathematics 01 natural sciences Contact point Fractal interpolation 010101 applied mathematics Set (abstract data type) Compatibility condition Mathematics (miscellaneous) Perspective (geometry) Simple (abstract algebra) System of iterative functional equations Compatibility (mechanics) Applied mathematics Affine transformation Uniqueness 0101 mathematics Mathematics |
| Zdroj: | Repositório Científico de Acesso Aberto de Portugal Repositório Científico de Acesso Aberto de Portugal (RCAAP) instacron:RCAAP |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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