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 32 条

[21] 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
[22] Algebraicity and transcendency of basic special values of Shintani's double sine functions
Kurokawa, Nobushige
Wakayama, Masato
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2006, 49 : 361 - 366
[23] Majorization Results for Subclasses of Starlike Functions Based on the Sine and Cosine Functions (10.1007/s41980-019-00262-y, 2019)
Tang, Huo
Srivastava, H. M.
Li, Shu-Hai
Deng, Guan-Tie
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2020, 46 (02) : 389 - 391
[24] On a generalization of Jacobi's elliptic functions and the double sine-Gordon kink chain
Pawellek, Michael
JOURNAL OF MATHEMATICAL PHYSICS, 2011, 52 (11)
[25] A SIMPLE PROOF OF ZAHORSKI'S DESCRIPTION OF NON-DIFFERENTIABILITY SETS OF LIPSCHITZ FUNCTIONS
Fowler, Thomas
Preiss, David
REAL ANALYSIS EXCHANGE, 2008, 34 (01) : 127 - 138
[26] A class of logarithmically completely monotonic functions and the best bounds in the second Kenshaw's double inequality
Qi, Feng
Guo, Bai-Ni
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2008, 212 (02) : 444 - 456
[27] A New Extension of Hardy-Hilbert's Inequality Containing Kernel of Double Power Functions
Yang, Bicheng
Wu, Shanhe
Chen, Qiang
MATHEMATICS, 2020, 8 (06)
[28] A class of logarithmically completely monotonic functions and the best bounds in the first Kershaw's double inequality
Qi, Feng
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 206 (02) : 1007 - 1014
[29] A Solution to Qi's Conjecture on a Double Inequality for a Function Involving the Tri- and Tetra-Gamma Functions
Matejicka, Ladislav
MATHEMATICS, 2019, 7 (11)
[30] REFINEMENTS OF KY FAN'S EIGENVALUE INEQUALITY FOR SIMPLE EUCLIDEAN JORDAN ALGEBRAS BY USING GRADIENTS OF K-INCREASING FUNCTIONS
Niezgoda, Marek
MATHEMATICAL INEQUALITIES & APPLICATIONS, 2021, 24 (04): : 1065 - 1065

← 1 2 3 4 →