Constructive Approximation

, Volume 45, Issue 2, pp 273–299

# Constructive Solutions for Systems of Iterative Functional Equations

• Cristina Serpa
• Jorge Buescu
Article

## 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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