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Flett’s mean value theorem for approximately differentiable functions. (English) Zbl 1081.26001
Summary: Flett’s mean value theorem states that if $$f$$ is differentiable on $$[a,b]$$ and $$f'(a)=f'(b)$$, then there is an $$\eta\in(a,b)$$ such that $$f (\eta)-f(a)= f'(\eta)(\eta-a)$$. In this article we prove an extension of this theorem and some of its variants. In particular, we show that the conclusions continue to hold for approximately differentiable functions.

##### MSC:
 26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems