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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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