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- W3037909257 abstract "We define a 2-convex system by the restrictions $x_{1} + x_{2} + ldots + x_{n} = ns$, $e(x_{1}) + e(x_{2}) + ldots + e(x_{n}) = nk$, $x_{1} geq x_{2} geq ldots geq x_{n}$ where $e:I to RR$ is a strictly convex function. We study the variation intervals for $x_k$ and give a more general version of the Boyd-Hawkins inequalities. Next we define a majorization relation on $A_S$ by $xpreccurlyeq_p y$ $Leftrightarrow$ $T_k(x) leq T_k(y) forall 1 leq k leq p-1$ and $B_k(x) leq B_k(y) forall p+2 leq k leq n$ (for fixed $1 leq p leq n-1$) where $T_k(x) = x_1 + ldots + x_k$, $B_k(x) = x_k + ldots + x_n$. The following Karamata type theorem is given: if $x, y in A_S$ and $xpreccurlyeq_p y$ then $f(x_1) + f(x_2) + ldots + f(x_n) leq f(y_1) + f(y_2) + ldots + f(y_n)$ $forall$$f:I to RR$ 3-convex with respect to $e$. As a consequence, we get an extended version of the equal variable method of V. Cirtoaje" @default.
- W3037909257 created "2020-07-02" @default.
- W3037909257 creator A5001989484 @default.
- W3037909257 date "2020-06-01" @default.
- W3037909257 modified "2023-09-26" @default.
- W3037909257 title "Majorization in the Framework of 2-Convex Systems" @default.
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