On the Functional Inequality f (x)f (y) - f (xy) ≤ f (x) plus f (y) - f (x plus y)

被引：0

作者：

Alzer, Horst ^{[1
]}

Salinas, Luis ^{[2
,3
]}

机构：

[1] Morsbacher Str 10, D-51545 Waldbrol, Germany

[2] Univ Tecn Federico Santa Maria, Dept Informat, Valparaiso, Chile

[3] Univ Tecn Federico Santa Maria, CCTVal, Valparaiso, Chile

来源：

COMPUTATIONAL METHODS AND FUNCTION THEORY | 2020年 / 20卷 / 3-4期

关键词：

Functional inequality; Convex; Concave;

D O I：

10.1007/s40315-020-00327-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that all solutions f : R -> R of the functional inequality (*) f (x) f (y) - f (xy) <= f (x) + f (y) - f (x + y), which are convex or concave on R and differentiable at 0 are given by f (x) = x and f (x) c, where 0 <= c <= 2. Moreover, we show that the only non-constant solution f : R -> R of (*), which is continuous on R and differentiable at 0 with f (0) = 0 is f (x) = x.

引用

页码：623 / 627

页数：5

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