Abstract
The paper deals with the mean value theorem of differential and integral calculus due to Flett (Math Gazette 42:38–39, 1958) and its various extensions. Since this theorem is a source of interest in various fields of mathematics (including functional equations), we aim to provide a detailed study of various (known as well as new) sufficient conditions for its validity, their geometric interpretations, and a comparison of the corresponding classes of functions. Moreover, our approach enables many new alternative proofs of known results, for instance, Pawlikowska’s extension of Flett’s theorem for higher-order derivatives. Some interesting open problems are also formulated.
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This research was partially supported by Grants VVGS-2013-121 and VVGS-PF-2014-453.
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Hutník, O., Molnárová, J. On Flett’s mean value theorem. Aequat. Math. 89, 1133–1165 (2015). https://doi.org/10.1007/s00010-014-0311-5
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DOI: https://doi.org/10.1007/s00010-014-0311-5