Year: 2025
Type: article
Abstract: In this paper, we consider the global comparison problem of Gini means with fixed number of variables on a subinterval I of $$\mathbb {R}_+$$ R + , i.e., the following inequality where $$n\in \mathbb {N},n\ge 2$$ n ∈ N , n ≥ 2 is fixed, $$(p,q),(r,s)\in \mathbb {R}^2$$ ( p , q ) , ( r , s ) ∈ R 2 and $$x_1,\dots ,x_n\in I$$ x 1 , ⋯ , x n ∈ I . Given a nonempty subinterval I of $$\mathbb {R}_+$$ R + and $$n\in \mathbb {N}$$ n ∈ N , we introduce the relations $$\begin{aligned} \Gamma _n(I)&:=\{((r,s),(p,q))\in \mathbb {R}^2\times \mathbb {R}^2\mid (*) \text{ holds } \text{ for } \text{ all } x_1,\dots ,x_n\in I\}, \\ \Gamma _\infty (I)&:=\bigcap _{n=1}^\infty \Gamma _n(I). \end{aligned}$$ Γ n ( I ) : = { ( ( r , s ) , ( p , q ) ) ∈ R 2 × R 2 ∣ ( ∗ ) holds for all x 1 , ⋯ , x n ∈ I } , Γ ∞ ( I ) : = ⋂ n = 1 ∞ Γ
Source: Results in Mathematics
Authors: Richárd Grünwald, Zsolt Páles
Institution: University of Debrecen
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4407687652