scholarly journals Asymptotic behavior of intermediate points in the differential mean value theorem of divided differences with repetitions

2010 ◽  
Vol 365 (1) ◽  
pp. 358-362 ◽  
Author(s):  
Aimin Xu ◽  
Feng Cui ◽  
Zhicheng Hu
Keyword(s):  
Asymptotic Behavior ◽  
Mean Value ◽  
Divided Differences ◽  
Mean Value Theorem ◽  
Differential Mean Value Theorem

scholarly journals Exponential Stability of Periodic Solutions for Inertial Type BAM Cohen-Grossberg Neural Networks

2014 ◽  
Vol 2014 ◽  
pp. 1-19 ◽  
Author(s):  
Chunfang Miao ◽  
Yunquan Ke
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Mean Value ◽  
Mean Value Theorem ◽  
First Order ◽  
Inequality Technique ◽  
Variable Substitution ◽  
Differential Mean Value Theorem

The existence and exponential stability of periodic solutions for inertial type BAM Cohen-Grossberg neural networks are investigated. First, by properly choosing variable substitution, the system is transformed to first order differential equation. Second, some sufficient conditions that ensure the existence and exponential stability of periodic solutions for the system are obtained by constructing suitable Lyapunov functional and using differential mean value theorem and inequality technique. Finally, two examples are given to illustrate the effectiveness of the results.

scholarly journals Stabilization and Synchronization of Hyper-Chaotic Financial System Involved in Positive Interest Rate

2020 ◽  
Author(s):  
Ruofeng Rao
Keyword(s):  
Financial System ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Pulse Control ◽  
Delayed Effect ◽  
Control Effect ◽  
Lyapunov Function Method ◽  
Mathematical Difficulties ◽  
Market Feedback ◽  
Differential Mean Value Theorem

In real financial market, the delayed market feedback and the delayed effect of government macro-control are inevitable. And both the delay of market feedback and the delay of macro-control effect bring about the mathematical difficulties in studying stabilization and synchronization of the hyper-chaotic financial system. However, employing Lyapunov function method, differential mean value theorem, suitable bounded hypotheses and pulse control technology results in the globally asymptotical stabilization and synchronization criteria. It is the first paper to drive the stabilization and synchronization criteria under the assumptions of the double delays. Finally, numerical examples illuminate the effectiveness of the proposed methods.

scholarly journals Sensitivity of the “intermediate point” in the mean value theorem: an approach via the Legendre-Fenchel transformation

2021 ◽  
Vol 71 ◽  
pp. 114-120
Author(s):  
Jean-Baptiste Hiriart-Urruty
Keyword(s):  
Asymptotic Behavior ◽  
Convex Functions ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Intermediate Point ◽  
Mild Conditions ◽  
The Mean

We study the sensitivity, essentially the differentiability, of the so-called “intermediate point” c in the classical mean value theorem $ \frac{f(a)-f(b)}{b-a}={f}^{\prime}(c)$we provide the expression of its gradient ∇c(d,d), thus giving the asymptotic behavior of c(a, b) when both a and b tend to the same point d. Under appropriate mild conditions on f, this result is “universal” in the sense that it does not depend on the point d or the function f. The key tool to get at this result turns out to be the Legendre-Fenchel transformation for convex functions.

BOX DIMENSION OF A NONLINEAR FRACTAL INTERPOLATION CURVE

Fractals ◽  
2019 ◽  
Vol 27 (03) ◽  
pp. 1950023 ◽  
Author(s):  
SONG-IL RI
Keyword(s):  
Mean Value ◽  
Mean Value Theorem ◽  
Box Dimension ◽  
Fractal Interpolation ◽  
Monotone Property ◽  
Interpolation Curve ◽  
Function Convex ◽  
Differential Mean Value Theorem ◽  
Box Dimensions

In this paper, we present a delightful method to estimate the lower and upper box dimensions of a special nonlinear fractal interpolation curve. We use Rakotch contractibility and monotone property of function in the estimation of upper box dimension, and we use Rakotch contractibility, noncollinearity of interpolation points, nondecreasing property of function, convex (or concave) property of function and differential mean value theorem in the estimation of lower box dimension. In particular, we propose a well-founded conjecture motivated by our results.

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