On Flett's mean value theorem.

The paper deals with the mean value theorem of differential and integral calculus due to Flett (Math Gazette 42:38-39, ) 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. [ABSTRACT FROM AUTHOR]