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Tomasz Szostok 《Lithuanian Mathematical Journal》2018,58(1):95-103
We present a method of proving inequalities for convex functions with use of Stieltjes integral. First, we show how some well-known inequalities can be obtained, and then we show how new inequalities and stronger versions of some existing results can be obtained. 相似文献
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Results in Mathematics - We observe that the Hermite–Hadamard inequality written in the form $$f\left(\frac{x+y}{2}\right)\leq\frac{F(y)-F(x)}{y-x}\leq\frac{f(x)+f(y)}{2}$$ may be viewed as... 相似文献
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We deal with the functional equation motivated by quadrature rules of approximate integration. In previous results the solutions of this equation were found only in some particular cases. For example the coefficients λ i were supposed to be rational or the equation in question was solved only for n=2. In the current paper we do not assume any particular form of coefficients occurring in this equation and we allow n to be any positive integer. Moreover, we obtain a solution of our equation without any regularity assumptions concerning the functions f and F.
相似文献
$F(y)-F(x)=(y-x)\sum_{i=1}^n a_if(\lambda_ix+(1-\lambda_i)y),\quad x,y\in \mathbb {R}$
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Let E be a Euclidean space,
dim E 2. We say that
f : E
E preserves equilateral triangles if for all triples of
points x, y, z E
we have
We show that if E is a finite-dimensional Euclidean space,
dim E 2,
f:E
E is measurable and preserves
equilateral triangles, then it is a similarity transformation (an isometry
multiplied by a positive constant). Moreover, in spaces at least
three-dimensional we get a similarity transformation without any
regularity assumption. Some generalizations as well as some interesting examples are also
presented in the paper. 相似文献
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Aequationes mathematicae - We study the alienation problem for two general linear equations i.e. we compare the solutions of the system of equations $$\begin{aligned} \left\{ \begin{array}{l}\sum... 相似文献
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Nadhomi Timothy Okeke Chisom Prince Sablik Maciej Szostok Tomasz 《Aequationes Mathematicae》2021,95(6):1095-1117
Aequationes mathematicae - The classical result of L. Székelyhidi states that (under some assumptions) every solution of a general linear equation must be a polynomial function. It is known... 相似文献
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