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Hyers-Ulam stability of an  iterative  equation  for  strictly increasing continuous functions

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Abstract

The Hyers-Ulam stability of the iterative equation \(f^n=F\) for continuous functions F was studied under the assumptions that F is a homeomorphism on its range, and the equation has stability on its range. It is important to study the stability of the equation for homeomorphisms on intervals. In this paper, theorems on stability are obtained using the properties of monotonic approximate solutions. The method is based on the stability of two derived iterative equations.

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Acknowledgements

The authors thank the referees for their valuable comments and suggestions. The first author thanks the National Institute of Technology Karnataka, Surathkal, for supporting this work.

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Authors and Affiliations

  1. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu,  632 014, India

    Rajendran Palanivel

  2. Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Surathkal, Mangaluru,  575 025, India

    Veerapazham Murugan

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  1. Rajendran Palanivel
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  2. Veerapazham Murugan
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Correspondence to Rajendran Palanivel.

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Palanivel, R., Murugan, V. Hyers-Ulam stability of an  iterative  equation  for  strictly increasing continuous functions. Aequat. Math. 97, 575–595 (2023). https://doi.org/10.1007/s00010-022-00935-w

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  • DOI: https://doi.org/10.1007/s00010-022-00935-w

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