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Flett’s mean value theorem for holomorphic functions. (English) Zbl 1021.30003
In 1958, T.M. Flett proved the following mean value theorem: if \(f:[a,b]\rightarrow \mathbb{R}\) is differentiable and \(f'(a)=f'(b)\) then there exists \(\eta\in(a,b)\) such that \(f(\eta)-f(a)=(\eta-a)f'(\eta).\) Its complex version is not valid as the function \(f(z)=e^z-z\) shows.
In this paper the authors give a generalization of Flett’s mean value theorem for holomorphic functions.

MSC:
30A99 General properties of functions of one complex variable
26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems
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