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Flett’s mean value theorem in topological vector spaces. (English) Zbl 1006.58007
Starting point is a result of T. M. Flett [Math. Gaz. 42, 38-39 (1958)]. Namely that for every differentiable real valued function \(f\) on an interval \([a,b]\) with identical derivative at the endpoints there exists a point \(\eta\in[a,b]\) such that the tangent of \(f\) at \(\eta\) passes through the endpoint \((a,f(a))\).
Here it is shown that this can be adapted to situations where the assumption on the endpoints is not satisfied or the differentiability assumption is weakened. Furthermore a weak version of this for topological vector space valued functions is given.
Reviewer: A.Kriegl (Wien)

58C20 Differentiation theory (Gateaux, Fréchet, etc.) on manifolds
26E20 Calculus of functions taking values in infinite-dimensional spaces
46G05 Derivatives of functions in infinite-dimensional spaces
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