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Solving functional equations via finite substitutions

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Abstract

In this paper, we study single variable functional equations that involve one unknown function and a finite set of known functions that form a group under the operation of composition. The main theorems give sufficient conditions for the existence and uniqueness of a (local) solution and also stability-type result for the solution. In the proofs, besides the standard methods of classical analysis, some group theoretical tools play a key role.

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Authors and Affiliations

  1. Institute of Mathematics, University of Debrecen, Pf. 12, 4010, Debrecen, Hungary

    Mihály Bessenyei

  2. Faculty of Engineering, University of Debrecen, Pf. 12, 4010, Debrecen, Hungary

    Csaba G. Kézi

Authors
  1. Mihály Bessenyei
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  2. Csaba G. Kézi
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Corresponding author

Correspondence to Mihály Bessenyei.

Additional information

Dedicated to the 60th birthday of Professor László Székelyhidi

This research has been supported by the Hungarian Scientific Research Fund (OTKA) Grants NK-81402.

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Bessenyei, M., Kézi, C.G. Solving functional equations via finite substitutions. Aequat. Math. 85, 593–600 (2013). https://doi.org/10.1007/s00010-012-0176-4

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  • DOI: https://doi.org/10.1007/s00010-012-0176-4

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