Results 111 to 120 of about 64,486 (162)
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Journal of Mathematical Sciences, 2012
The author proves several extensions of the well-known Lagrange mean value theorem for cases of continuous functions on the real line and in the complex plane. The paper starts with integrating (Denjoy) the equations in the Lagrange mean value theorem and recognizing that the slope of the chord through \((a,f(a))\) and \((b,f(b))\) is equal to the ...
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The author proves several extensions of the well-known Lagrange mean value theorem for cases of continuous functions on the real line and in the complex plane. The paper starts with integrating (Denjoy) the equations in the Lagrange mean value theorem and recognizing that the slope of the chord through \((a,f(a))\) and \((b,f(b))\) is equal to the ...
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ON THE FRACTIONAL MEAN-VALUE THEOREM
International Journal of Bifurcation and Chaos, 2012In 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
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Ukrainian Mathematical Journal, 2014
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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, 2020Let 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′(...
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A Restricted Mean Value Theorem
Journal of the London Mathematical Society, 1969For each prime \(p\) let \(f(p)\) denote the least integer solution \(n\) to the Legendre character conditions \[ \left(\frac{n+a_j}{p}\right) = \varepsilon_j, \quad (j=1,\ldots,k). \] Elliott shows that there exist positive constants \(\alpha\), \(A\) so that \[ \left(\sum_{p\le x} \min(f(p),x^\alpha)\right)/\pi(x) \rightarrow A\quad\text{as }x\to ...
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On a Certain Mean Value Theorem
Moscow University Mathematics Bulletin, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The American Mathematical Monthly, 1999
Several theorems go by this name. The present note adds to the assortment an unusual variant (Theorem 1), which involves the shape of the underlying region in an interesting way. We work in Euclidean spaces, although Lemma 2 and the second inequality of Lemma 3 carry over to general Riemannian manifolds.
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Several theorems go by this name. The present note adds to the assortment an unusual variant (Theorem 1), which involves the shape of the underlying region in an interesting way. We work in Euclidean spaces, although Lemma 2 and the second inequality of Lemma 3 carry over to general Riemannian manifolds.
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2002
The derivative of a function f at a point ξ $$f'\left( \xi \right) = \mathop {\lim }\limits_{\Delta x \to 0} {\rm{ }}{{f\left( {\xi + \Delta x} \right) - f\left( \xi \right)} \over {\Delta x}},$$ is the slope of the line tangent to the graph of f at the point P = (ξ ,f (ξ)).
Adi Ben-Israel, Robert Gilbert
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The derivative of a function f at a point ξ $$f'\left( \xi \right) = \mathop {\lim }\limits_{\Delta x \to 0} {\rm{ }}{{f\left( {\xi + \Delta x} \right) - f\left( \xi \right)} \over {\Delta x}},$$ is the slope of the line tangent to the graph of f at the point P = (ξ ,f (ξ)).
Adi Ben-Israel, Robert Gilbert
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Mean-Value Theorems in Arithmetic Semigroups
Acta Mathematica Hungarica, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lucht, L. G., Reifenrath, K.
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The American Mathematical Monthly, 1969
(1969). On Mean Value Theorems. The American Mathematical Monthly: Vol. 76, No. 1, pp. 70-73.
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(1969). On Mean Value Theorems. The American Mathematical Monthly: Vol. 76, No. 1, pp. 70-73.
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