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Une variante du theoreme de Cauchy de la valeur moyenne

100%

Wachnicki E.

2000

tom Vol. 33, nr 4

737-740

Dans cette note on demontre une variante du theoreme de Cauchy de la valeur moyenne.

Numerical treatment of the generalized time-fractional Huxley-Burgers’ equation and its stability examination

63%

Hadhoud A. R. , Alaal F. E. A. , Abdelaziz A. A. , Radwan T.

tom Vol. 54, nr 1

436--451

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.

A Cauchy-type generalization of Flett's theorem

63%

Markov L.

tom Vol. 54, nr 1

500--509

We prove a Cauchy-type generalization of Flett’s theorem and note its geometric interpretations. Several other mean value theorems extending further the result, which involve both real and complex functions, are also proved.

Mean-value theorems and some symmetric means

51%

Matkowski J.

Demonstratio Mathematica

2013

tom Vol. 46, nr 3

461--474

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.