Results 231 to 240 of about 745,922 (284)

On the mean value theorem

Optimization, 1988
Mean value theorems for nonsmooth functions are presented. Two versions are given, both using the contingent derivative. In. the first one a tangential convexity condition is used. In the second one no convexity assumption is made but the estimate. involves the contingent derivative df (x, b − a) of f at points arbitrarily close to the segment [a, b ...
exaly   +2 more sources

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

Mean-Value Theorem

Ukrainian Mathematical Journal, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

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

On a Certain Mean Value Theorem

Moscow University Mathematics Bulletin, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

A Restricted Mean Value Theorem

Journal of the London Mathematical Society, 1969
For 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 ...
openaire   +1 more source

A Mean Value Theorem

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.
openaire   +1 more source

Mean-Value Theorems in Arithmetic Semigroups

Acta Mathematica Hungarica, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lucht, L. G., Reifenrath, K.
openaire   +2 more sources