Zobrazeno 1 - 10
of 33
pro vyhledávání: '"26D15, 26D20"'
Autor:
Pinelis, Iosif
Based on an apparently new Lagrange-type identity, a Cauchy--Schwarz-type inequality is proved. The mentioned identity is obtained by using certain ``macro'' variables; it is hoped that such a method can be used to prove or produce other identities a
Externí odkaz:
http://arxiv.org/abs/2303.03310
Autor:
Sadov, Sergey
A review of author's work on cyclic inequalities of Shapiro-Diananda type and related optimization problems is presented.
Comment: 22 pp
Comment: 22 pp
Externí odkaz:
http://arxiv.org/abs/2212.05968
Autor:
Sadov, Sergey
The function $\inf_n nx^{1/n}$ has the asymptotics $eu+e d^2(u)/(2u)+O(1/u^2)$ as $x\to\infty$, where $u=\log x$ and $d(u)$ is the distance from $u$ to the nearest integer. We generalize this observation. First, the curves $y=nx^{1/n}$ can be written
Externí odkaz:
http://arxiv.org/abs/2210.07614
Autor:
Sadov, Sergey
Let $\mathbf{x}=(x_1,\dots,x_n)$ be an $n$-tuple of positive real numbers and the sequence $(x_i)_{i\in\mathbb{Z}}$ be its $n$-periodic extension. Given an $n$-tuple $\mathbf{r}=(r_1,\dots,r_n)$ of positive integers, let $a_i$ be the arithmetic mean
Externí odkaz:
http://arxiv.org/abs/2210.00360
Autor:
Wang, Liuquan
We denote by $c_t^{(m)}(n)$ the coefficient of $q^n$ in the series expansion of $(q;q)_\infty^m(q^t;q^t)_\infty^{-m}$, which is the $m$-th power of the infinite Borwein product. Let $t$ and $m$ be positive integers with $m(t-1)\leq 24$. We provide as
Externí odkaz:
http://arxiv.org/abs/2108.03932
Autor:
Czarnecki, Andrzej, Kiciński, Gabriel
We prove that the cyclic inequality $\sum\limits_{i=1}^{i=n}\left(\frac{x_i}{x_{i+1}}\right)^k\geq\sum\limits_{i=1}^{i=n}\frac{x_i}{x_{\sigma(i)}}$ holds for $k$ in a specific range dependant on the permutation $\sigma$. We also show that the same is
Externí odkaz:
http://arxiv.org/abs/2004.08882
Autor:
Pinelis, Iosif
A notion of generalized $n$-semimodularity is introduced, which extends that of (sub/super)mod\-ularity in four ways at once. The main result of this paper, stating that every generalized $(n\colon\!2)$-semimodular function on the $n$th Cartesian pow
Externí odkaz:
http://arxiv.org/abs/1902.05520
Autor:
Pinelis, Iosif
Exact lower and upper bounds on the best possible misclassification probability for a finite number of classes are obtained in terms of the total variation norms of the differences between the sub-distributions over the classes. These bounds are comp
Externí odkaz:
http://arxiv.org/abs/1712.00812
Autor:
Qi, Feng, Mortici, Cristinel
Publikováno v:
Applied Mathematics and Computation 271 (2015), 502--511
In the paper, the authors establish three kinds of double inequalities for the trigamma function in terms of the exponential function to powers of the digamma function. These newly established inequalities extend some known results. The method in the
Externí odkaz:
http://arxiv.org/abs/1503.03020
Autor:
Xi, Bo-Yan, Qi, Feng
Publikováno v:
Journal of Nonlinear and Convex Analysis 16 (2015), no. 5, 873--890
In the paper, the authors introduce a new concept "extended $s$-convex functions", establish some new integral inequalities of Hermite-Hadamard type for this kind of functions, and apply these inequalities to derive some inequalities of special means
Externí odkaz:
http://arxiv.org/abs/1406.5409