A SIMPLE PROOF OF OPPENHEIM'S DOUBLE INEQUALITY RELATING TO THE COSINE AND SINE FUNCTIONS

被引：8

作者：

Qi, Feng ^{[1
]}

Luo, Qiu-Ming ^{[2
]}

Guo, Bai-Ni ^{[3
]}

机构：

[1] Inner Mongolia Univ Nationalities, Coll Math, Tongliao City 028043, Inner Mongolia, Peoples R China

[2] Chongqing Normal Univ, Dept Math, Chongqing 401331, Peoples R China

[3] Henan Polytech Univ, Sch Math & Informat, Jiaozuo City 454010, Henan Province, Peoples R China

来源：

JOURNAL OF MATHEMATICAL INEQUALITIES | 2012年 / 6卷 / 04期

关键词：

Simple proof; Oppenheim's double inequality; cosine function; sine function; monotonicity; JORDANS INEQUALITY;

D O I：

10.7153/jmi-06-63

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the paper, the authors provide a simple proof of Oppenheim's double inequality relating to the cosine and sine functions. In passing, the authors survey this topic.

引用

页码：645 / 654

页数：10

共 4 条

[1] SHARPENING AND GENERALIZATIONS OF CARLSON'S DOUBLE INEQUALITY FOR THE ARC COSINE FUNCTION
Zhao, Jiao-Lian
Wei, Chun-Fu
Guo, Bai-Ni
Qi, Feng
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, 2012, 41 (02): : 201 - 209
[2] Optimal young's inequality and its converse: a simple proof
F. Barthe
Geometric & Functional Analysis GAFA, 1998, 8 : 234 - 242
[3] Optimal Young's inequality and its converse: A simple proof
Barthe, F
GEOMETRIC AND FUNCTIONAL ANALYSIS, 1998, 8 (02) : 234 - 242
[4] Sharpening and generalizations of Shafer-Fink's double inequality for the arc sine function
Guo, Bai-Ni
Luo, Qiu-Ming
Qi, Feng
FILOMAT, 2013, 27 (02) : 261 - 265

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