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ON THE FRACTIONAL MEAN-VALUE THEOREM

International Journal of Bifurcation and Chaos, 2012
In this paper, we derive a fractional mean-value theorem both in the sense of Riemann–Liouville and in the sense of Caputo. This new formulation is more general than the generalized Taylor's formula of Kolwankar and the fractional mean-value theorem in the sense of Riemann–Liouville developed by Trujillo.
Peng Guo, Changpin Li, Guanrong Chen
openaire   +2 more sources

Means and the mean value theorem

International Journal of Mathematical Education in Science and Technology, 2009
Let I be a real interval. We call a continuous function μ : I × I → ℝ a proper mean if it is symmetric, reflexive, homogeneous, monotonic and internal. Let f : I → ℝ be a differentiable and strictly convex or strictly concave function. If a, b ∈ I with a ≠ b, then there exists a unique number ξ between a and b such that f(b) − f(a) = f ′(ξ)(b − a).
Jorma K. Merikoski   +2 more
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Mean-Value Theorem

Ukrainian Mathematical Journal, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A New Proof of the Equivalence of the Cauchy Mean Value Theorem and the Mean Value Theorem

The American Mathematical Monthly, 2020
Let f,g:[a,b]→R be differentiable in (a, b) and continuous in [a,b] . The Cauchy mean value theorem states that, if g′(x)≠0 in (a, b), there is a number c∈(a,b) such that (1) f(b)−f(a)g(b)−g(a)=f′(...
openaire   +1 more source

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