Compatibility conditions for systems of iterative functional equations with non-trivial contact sets

• Autor(a) principal: Buescu, Jorge
• Data de Publicação: 2021
• Outros Autores: Serpa, Cristina
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10400.21/13217
• topic: Compatibility condition; System of iterative functional equations; Fractal interpolation; Contact point; Contact set

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.