相关论文: Characterizations of the equality of two-variable …

The purpose of this paper is to extend the definition of quasiarithmetic means by taking a strictly monotone generating function instead of a strictly monotone and continuous one. We establish the properties of such means and compare them…

The purpose of this paper is to establish several necessary and sufficient conditions to ensure the validity of a general functional inequality in terms of generalized quasi-arithmetic means. In particular cases, we consider H\"older-,…

The aim of this paper is to investigate inequalities that are analogous to the Minkowski and H\"older inequalities by replacing the addition and the multiplication by a more general operation, and instead of using power means, generalized…

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…

Based on collection of bijections, variable and function are extended into ``isomorphic variable'' and ``dual-variable-isomorphic function'', then mean values such as arithmetic mean and mean of a function are extended to ``isomorphic…

Let $I\subseteq\mathbb{R}$ be a nonempty open subinterval. We say that a two-variable mean $M:I\times I\to\mathbb{R}$ enjoys the \emph{balancing property} if, for all $x,y\in I$, the equality \begin{equation}\tag{1}…

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…

The aim of this paper is to introduce several notions of homogenization in various classes of weighted means, which include quasiarithmetic and semideviation means. In general, the homogenization is an operator which attaches a homogeneous…

In this paper, the bivariate log-convexity of the two-parameter homogeneous function in parameter pair is vestigated. From this the bivariate log-convexity of the more extended means with respect to a parameter pair is solved. It follows…

In this paper we characterize generalized quasi-arithmetic means, that is means of the form $M(x_1,...,x_n):=(f_1+...+f_n)^{-1}(f_1(x_1)+...+f_n(x_n))$, where $f_1,...,f_n:I\to\mathbb{R}$ are strictly increasing and continuous functions.…

The purpose of this paper is to investigate the following invariance equation involving two $2$-variable generalized Bajraktarevi\'c means, i.e., we aim to solve the functional equation $$…

The aim of this paper is to characterize the so-called $\sigma$-balancing property in the class of generalized quasi-arithmetic means. In general, the question is whether those elements of a given family of means that possess this property…

The theory of quasi-arithmetic means is a powerful tool in the study of covariance functions across space-time. In the present study we use quasi-arithmetic functionals to make inferences about the permissibility of averages of functions…

The purpose of this paper is to investigate the equality problem of generalized Bajraktarevi\'c means, i.e., to solve the functional equation \begin{equation}\label{E0}\tag{*}…

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)…

We define decision-making functions which arise from studying the multidimensional generalization of the weighted Bajraktarevi\'c means. It allows a nonlinear approach to optimization problems. These functions admit several interesting…

Quasi-arithmetic means are defined for every continuous, strictly monotone function $f \colon U \rightarrow \mathbb{R}$, ($U$ -- an interval). For an $n$-tuple $a \in U^n$ with corresponding vector of weights $w=(w_1,\dots,w_n)$ ($w_i>0$,…

In recent papers the convexity of quasiarithmetic means was characterized under twice differentiability assumptions. One of the main goals of this paper is to show that the convexity or concavity of a quasiarithmetic mean implies the the…

We provide sufficient conditions of P\'olya type which guarantee the positive definiteness of a $2\times 2$-matrix-valued function in $\mathbb{R}$ and $\mathbb{R}^3$. Several bivariate covariance models have been proposed in literature,…

In 1938, Gini studied a mean having two parameters. Later, many authors studied properties of this mean. It contains as particular cases the famous means such as harmonic, geometric, arithmetic, etc. Also it contains, the power mean of…