A ONE-PARAMETER FAMILY OF BIVARIATE MEANS

被引：20

作者：

Neuman, Edward ^{[1
]}

机构：

[1] So Illinois Univ, Dept Math, Carbondale, IL 62901 USA

来源：

JOURNAL OF MATHEMATICAL INEQUALITIES | 2013年 / 7卷 / 03期

关键词：

Bivariate means; Seiffert means; Neuman-Sandor mean; logarithmic mean; Schwab-Borchardt mean; inequalities; convex combinations; INEQUALITIES; BOUNDS;

D O I：

10.7153/jmi-07-35

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A one-parameter family of bivariate means is introduced. Members of the new family of means are derived from a bivariate symmetric mean. It is shown that new means are symmetric in their variables. Several inequalities involving parametric versions of two Seiffert means, the Neuman-Sandor mean, and the logarithmic means are obtained. It is shown that the last four means belong to the family of the Schwab-Borchardt means. Among inequalities established in this paper some provide generalizations of known results obtained recently by several researchers.

引用

页码：399 / 412

页数：14

共 23 条

[1]

[Anonymous], NIEUW ARCH WISK

[2]

[Anonymous], ANAL INEQUALITIES

[3]

[Anonymous], J INEQUAL APPL

[4]

[Anonymous], PREPRINT

[5]

[Anonymous], MATH INEQUA IN PRESS

[6]

[Anonymous], 2012, ADV INEQUAL APPL

[7]

[Anonymous], 1995, WURZEL

[8]

[Anonymous], INT J PURE APPL MATH

[9]

Borwein J., 1987, Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity

[10] ALGORITHMS INVOLVING ARITHMETIC AND GEOMETRIC MEANS [J].

CARLSON, BC .

AMERICAN MATHEMATICAL MONTHLY, 1971, 78 (05) :496-&

← 1 2 3 →