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 X, Y 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.
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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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Communicated by Wolfgang Dahmen.
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Serpa, C., Buescu, J. Constructive Solutions for Systems of Iterative Functional Equations. Constr Approx 45, 273–299 (2017). https://doi.org/10.1007/s00365-016-9349-z
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DOI: https://doi.org/10.1007/s00365-016-9349-z