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A Flett Theorem for the Riemann–Stieltjes Integral

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Abstract

By employing Riesz decomposition theorem about monotone functions, we prove a Flett type theorem for the Riemann–Stieltjes integral and related integral mean value results. Then, since monotone functions are inner functions for gauge integrable functions, we revisit classical mean value integral theorems in terms of the gauge integral.

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  1. UMR 8542 – Laboratoire Paul Painlevé, Université de Lille, 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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Vîjîitu, V. A Flett Theorem for the Riemann–Stieltjes Integral. Results Math 79, 34 (2024). https://doi.org/10.1007/s00025-023-02062-7

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  • DOI: https://doi.org/10.1007/s00025-023-02062-7

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