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On the equality of generalized Bajraktarevi\'c means under first-order differentiability assumptions
Autor:
Páles, Zsolt, Zakaria, Amr
In this paper we consider the equality problem of generalized Bajraktarevi\'c means, i.e., we are going to solve the functional equation \begin{equation}\label{E0}\tag{*} f^{(-1)}\bigg(\frac{p_1(x_1)f(x_1)+\dots+p_n(x_n)f(x_n)}{p_1(x_1)+\dots+p_n(x_n
Externí odkaz:
http://arxiv.org/abs/2410.16074
Autor:
Páles, Zsolt, Zakaria, Amr
The equality problem of the two-variable Bajraktarevi\'c means can be expressed as the functional equation $$ \left(\frac{f}{g}\right)^{-1}\bigg(\frac{f(x)+f(y)}{g(x)+g(y)}\bigg) =\left(\frac{h}{k}\right)^{-1}\bigg(\frac{h(x)+h(y)}{k(x)+k(y)}\bigg)\q
Externí odkaz:
http://arxiv.org/abs/2112.07396
Autor:
Páles, Zsolt, Zakaria, Amr
This paper is motivated by an astonishing result of H. Alzer and S. Ruscheweyh published in 2001 in the Proc. Amer. Math. Soc., which states that the intersection of the classes two-variable Gini means and Stolarsky means is equal to the class of two
Externí odkaz:
http://arxiv.org/abs/2012.03588
Autor:
Páles, Zsolt, Zakaria, Amr
In this note, we present an extension of the celebrated Abel-Liouville identity in terms of noncommutative complete Bell polynomials for generalized Wronskians. We also characterize the range equivalence of $n$-dimensional vector-valued functions in
Externí odkaz:
http://arxiv.org/abs/2009.01639
Given two functions $f,g:I\to\mathbf{R}$ and a probability measure $\mu$ on the Borel subsets of $[0,1]$, the two-variable mean $M_{f,g;\mu}:I^2\to I$ is defined by $$ M_{f,g;\mu}(x,y) :=\bigg(\frac{f}{g}\bigg)^{-1}\left( \frac{\int_0^1 f\big(tx+(1-t
Externí odkaz:
http://arxiv.org/abs/1912.10111
The main result of this paper provides six necessary and sufficient conditions under various regularity assumptions for a so-called Cauchy mean to be identical to a two-variable quasiarithmetic mean. One of these conditions says that a Cauchy mean is
Externí odkaz:
http://arxiv.org/abs/1907.09186
Autor:
Páles, Zsolt, Zakaria, Amr
This paper offers a solution of the functional equation $$ \big(tf(x)+(1-t)f(y)\big)\varphi(tx+(1-t)y)=tf(x)\varphi(x)+(1-t)f(y)\varphi(y) \qquad(x,y\in I), $$ where $t\in\,]0,1[\,$ is a fixed number, $\varphi:I\to\mathbb{R}$ is strictly monotone, an
Externí odkaz:
http://arxiv.org/abs/1904.12612
Autor:
Páles, Zsolt, Zakaria, Amr
Publikováno v:
Aequationes Math. 93(1-2) (2019), 37--57
The purpose of this paper is to investigate the invariance of the arithmetic mean with respect to two weighted Bajraktarevi\'c means, i.e., to solve the functional equation $$ \bigg(\frac{f}{g}\bigg)^{\!\!-1}\!\!\bigg(\frac{tf(x)+sf(y)}{tg(x)+sg(y)}\
Externí odkaz:
http://arxiv.org/abs/1801.00989
Autor:
Páles Zsolt, Zakaria Amr
Publikováno v:
Annales Mathematicae Silesianae, Vol 36, Iss 2, Pp 206-214 (2022)
In this note, we present an extension of the celebrated Abel– Liouville identity in terms of noncommutative complete Bell polynomials for generalized Wronskians. We also characterize the range equivalence of n-dimensional vector-valued functions in
Externí odkaz:
https://doaj.org/article/8d6192a7f38141209a4e3987c1c15470
Publikováno v:
In International Immunopharmacology August 2022 109