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A note on Oscar Chisini mean value definition
mean value integral geometry Erlanger Programm
2016/5/30
Mainly on the basis of some notable physical problems reported in a 1929 Oscar Chisini paper, this brief note expose further possible historic-critical remarks on the definition of statistical mean va...
Mean value properties of harmonic functions on Sierpinski gasket type fractals
Sierpinski gasket Laplacian harmonic function mean value property analysis on fractals
2012/6/27
In this paper, we establish an analogue of the classical mean value property for both the harmonic functions and some general functions in the domain of the Laplacian on the Sierpinski gasket. Further...
Abstract: For the positive integer $n$, let $f(n)$ denote the number of positive integer solutions $(n_1, n_2, n_3)$ of the Diophantine equation $$ {4\over n}={1\over n_1}+{1\over n_2}+{1\over n_3}. $...
On generalized Flett's mean value theorem
Flett’s mean value theorem real function differentiability Taylor polynomial
2011/9/13
Abstract: We present a new proof of generalized Flett's mean value theorem due to Pawlikowska (from Demonstratio Math. 1999) using only the original Flett's mean value theorem. Also, a Trahan-type con...
An identity on the $2m$-th power mean value of the generalized Gauss sums
2m-th power mean exact calculating formula generalized quadratic Gauss sums Number Theory
2011/9/5
Abstract: In this paper, using combinatorial and analytic methods, we prove an exact calculating formula on the $2m$-th power mean value of the generalized quadratic Gauss sums for $m\geq 2$. This sol...
A mean value formula for elliptic curves
elliptic curves Weierstrass ℘ -function point multiplication division polynomial
2011/8/24
Abstract: It is proved in this paper that for any point on an elliptic curve, the mean value of x-coordinates of its n-division points is the same as its x-coordinate and that of y-coordinates of its ...
The mean value for infinite volume measures, infinite products and heuristic infinite dimensional Lebesgue measures
The mean value for infinite volume measures infinite products heuristic infinite dimensional Lebesgue measures
2011/1/20
The goal of this article is to define the mean value of a function defined on an infinite product of measured spaces with infinite measure. As a preliminary approach, the mean value of a map defined o...
R. Feng, and H. Wu recently established a certain mean-value formula
for the x-coordinates of the n-division points on an elliptic curve given in
Weierstrass form (A mean value formula for elliptic ...
A mean value formula for elliptic curves
elliptic curves point multiplication division polynomial
2009/12/29
It is proved in this paper that for any point on an elliptic curve,
the mean value of x-coordinates of its n-division points is the same as
its x-coordinate.
An Inequality of Ostrowski Type via Pompeiu's Mean Value Theorem
Ostrowski's inequality Pompeiu mean value theorem quadrature rules Special means
2008/7/2
An inequality providing some bounds for the integral mean via Pompeiu's mean value theorem and applications for quadrature rules and special means are given.
Generalizations of the Trapezoid Inequalities Based on a New Mean Value Theorem for the Remainder in Taylor's Formula
Classical trapezoid inequality Perturbed trapezoid inequality Mean value theorem Generalizations
2008/7/1
Generalizations of the classical and perturbed trapezoid inequalities are developed using a new mean value theorem for the remainder in Taylor's formula. The resulting inequalities for N-times differe...
New Ostrowski Type Inequalities Via Mean Value Theorems
Ostrowski type inequalities Mean value theorems Differentiable Integrable function identities Properties of modulus
2008/6/30
The main aim of the present note is to establish two new Ostrowski type inequalities by using the mean value theorems.
On an Upper Bound for the Deviations from the Mean Value
Arithmetic mean Square mean Cauchy-Schwarz-Buniakovski inequality Triangle inequality
2008/6/30
A completely elementary proof of a known upper bound for the deviations from the mean value is given. Related inequalities are also discussed. Applications to triangle inequalities provide characteriz...
On Grüss Like Integral Inequalities via Pompeiu's Mean Value Theorem
Grüss like integral inequalities Pompeiu's mean value theorem Lagrange's mean value theorem Differentiable Properties of modulus
2008/6/30
In the present note we establish two new integral inequalities similar to that of the Grüss integral inequality via Pompeiu's mean value theorem.
On Some New Mean Value Inequalities
Mean value inequality Hö lder's inequality Continuous positive function Extension
2008/6/27
In this paper, using the arithmetic-geometric mean inequality, we obtain some new mean value inequalities. Finally, some applications are given, they are extension of Hölder's inequalities.