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Hyers-Ulam stability of mean value points

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Abstract

We extend and simplify proofs of some recent results on stability in the sense of Hyers and Ulams for mean value points that come from differential expressions, like Rolle theorem and co. Then, classical mean value theorems due to Lagrange and Cauchy are generalized in the setting of divided differences with multiplicities and we prove Hyers-Ulam stability for the corresponding mean value points.

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Acknowledgements

The author would like to thank the anonymous referee for carefully reading of the manuscript and for bringing to his attention the paper quoted in [16].

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  1. Université de Lille, Laboratoire Paul Painlevé, 59655, Villeneuve d’Ascq Cedex, France

    Viorel Vîjîitu

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  1. Viorel Vîjîitu
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Correspondence to Viorel Vîjîitu.

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Communicated by Gerald Teschl.

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Vîjîitu, V. Hyers-Ulam stability of mean value points. Monatsh Math (2024). https://doi.org/10.1007/s00605-024-01987-7

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