New means of Cauchy's type

被引：19

作者：

Anwar, Matloob ^{[1
]}

Pecaric, J. ^{[1
,2
]}

机构：

[1] GC Univ, Abdus Salam Sch Math Sci, Lahore Gulberg 54660, Pakistan

[2] Univ Zagreb, Fac Text Technol, Zagreb 10000, Croatia

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2008年 / 2008卷 / 1期

关键词：

Full Article; Publisher Note;

D O I：

10.1155/2008/163202

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We will introduce new means of Cauchy's type M(r,l)(s) (f, mu) defined, for example, as M(r,l)(s) (f, mu) = ((l(l-s)/r(r-s))(M(r)(r)(f, mu) - M(s)(r)(f, mu)/M(l)(l)(f, mu)-M(s)(l)(f, mu)))(1/(r-l)),in the case when l not equal r not equal s, l, r not equal 0. We will show that this new Cauchy's mean is monotonic, that is, the following result. Theorem. Let t, r, u, v is an element of R, such that t <= v, r <= u. Then forM(r,l)(s) (f, mu), one has M(t,r)(s) <= M(v,u)(s). We will also give some related comparison results. Copyright (C) 2008 M. Anwar.

引用

页数：10