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1
Content available remote Numerical treatment of the generalized time-fractional Huxley-Burgers’ equation and its stability examination
Hadhoud Adel R., Alaal Faisal E. Abd, Abdelaziz Ayman A., Radwan Taha
Demonstratio Mathematica
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2021
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Vol. 54, nr 1
436--451
EN
In this paper, we show how to approximate the solution to the generalized time-fractional Huxley-Burgers’ equation by a numerical method based on the cubic B-spline collocation method and the mean value theorem for integrals. We use the mean value theorem for integrals to replace the time-fractional derivative with a suitable approximation. The approximate solution is constructed by the cubic B-spline. The stability of the proposed method is discussed by applying the von Neumann technique. The proposed method is shown to be conditionally stable. Several numerical examples are introduced to show the efficiency and accuracy of the method.
2
Content available remote Mean-value theorems and some symmetric means
Matkowski J.
Demonstratio Mathematica
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2013
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Vol. 46, nr 3
461--474
EN
Some variants of the Lagrange and Cauchy mean-value theorems lead to the conclusion that means, in general, are not symmetric. They are symmetric iff they coincide (respectively) with the Lagrange and Cauchy means. Under some regularity assumptions, we determine the form of all the relevant symmetric means.
3
Content available remote Mean-value theorems for one-sided differentiable functions
Wituła R., Hetmaniok E., Słota D.
Fasciculi Mathematici
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2012
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Nr 48
145--154
EN
We show that Kubik's generalizations of the classical mean-value theorems for one-sided differentiable functions are equivalent to those of Karamata and Vučkovič. Some applications of these theorems are presented.
4
Content available remote Mean-value type equalities with interchanged function and derivative
Matkowski J.
Fasciculi Mathematici
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2011
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Nr 47
19--27
EN
According to a new mean value-theorem, if a func¬tion f satisfies the classical conditions ensuring the existence and uniqueness of Lagrange’s mean, then there also exists a unique mean M such that ...[wzór]. The main result gives necessary and sufficient conditions for the equality ...[wzór] The relevant equality for the Lagrange mean-value theorem is also considered.
5
Content available remote Generalizations of Lagrange and Cauchy Mean-Value theorems
Matkowski J.
Demonstratio Mathematica
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2010
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Vol. 43, nr 4
765-774
EN
Some generalizations of the Lagrange Mean-Value Theorem and Cauchy Mean-Value Theorem are proved and the extensions of the corresponding classes of means are presented.
6
Content available remote Towards historical roots of necessary conditions of optimality: Regula of Peano
Dolecki S., Greco G. H.
Control and Cybernetics
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2007
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Vol. 36, no 3
491-518
EN
At the end of 19th century Peano discerned vector spaces, differentiability, convex sets, limits of families of sets, tangent cones, and many other concepts, in a modern perfect form. He applied these notions to solve numerous problems. The theorem on necessary conditions of optimality (Regula) is one of these. The formal language of logic that he developed, enabled him to perceive mathematics with great precision and depth. Actually he built mathematics axiomatically based exclusively on logical and set-theoretic primitive terms and properties, which was a revolutionary turning point in the development of mathematics.
7
Content available remote Local cone approximations in optimization
Castellani M., Pappalardo M.
Control and Cybernetics
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2007
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Vol. 36, no 3
583-600
EN
We show how to use intensively local cone approximations to obtain results in some fields of optimization theory such as optimality conditions, constraint qualifications, mean value theorems and error bound.
8
Content available remote A note on a Cauchy-type mean value theorem
Ivan M.
Demonstratio Mathematica
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2002
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Vol. 35, nr 3
493-494
EN
We prove that a Cauchy-type mean value theorem [E. Wachnicki, Une variante du theoreme de Cauchy de la valeur moyenne, Demonstratio Math., 33 (4) (2000), 737-740] is a particular case of Flett's Mean Value Theorem [T. M. Flett, A mean value theorem, Math. Gazette 42 (1958), 38-39].
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