Constructive Approximation

, Volume 45, Issue 2, pp 273–299 | Cite as

Constructive Solutions for Systems of Iterative Functional Equations

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Abstract

We formulate a general theoretical framework for systems of iterative functional equations between general spaces X and Y. We find general necessary conditions for the existence of solutions. When X and Y are topological spaces, we characterize continuity of solutions; when XY are metric spaces, we find sufficient conditions for existence and uniqueness. For finite-order systems, we construct explicit formulae for the solution. We provide an extended list of examples, including fractal interpolation functions, which are covered by our general framework.

Keywords

Functional equation Explicit solution De Rham’s function Fractal interpolation Iteration methods 

Mathematics Subject Classification

39B72 39B12 28A80 41A05 

Notes

Acknowledgments

The authors gratefully acknowledge the valuable suggestions of the anonymous referees. The first author acknowledges support from Fundação para a Ciência e Tecnologia under Grant SFRH/BD/77623/2011. The second author was partially supported by FCT via UID/MAT/04561/2013.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Centro de Matemática Aplicações Fundamentais e Investigação Operacional, Faculdade de CiênciasUniversidade de LisboaLisbonPortugal

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