Necessary and sufficient conditions for the two parameter generalized Wilker-type inequalities

Journal of Inequalities and Applications

Zhen-Hang Yang¹  Yu-Ming Chu²  Hui Sun² 

[1] Department of Science and Technology, State Grid Zhejiang Electric Power Research Institute;School of Mathematics and Computation Sciences, Hunan City University;

关键词: Wilker-type inequality;    sine function;    tangent function;    necessary and sufficient condition;   

DOI  :  10.1186/s13660-016-1270-2

来源: DOAJ

【 摘 要 】

Abstract In the article, we provide the necessary and sufficient conditions for the parameters α and β such that the generalized Wilker-type inequality 2 β α + 2 β ( sin x x ) α + α α + 2 β ( tan x x ) β − 1 > ( < ) 0 $$ \frac{2\beta}{\alpha+2\beta} \biggl(\frac{\sin x}{x} \biggr)^{\alpha}+ \frac{\alpha}{\alpha+2\beta} \biggl(\frac{\tan x}{x} \biggr)^{\beta}-1>(< )0 $$ holds for all x ∈ ( 0 , π / 2 ) $x\in(0, \pi/2)$ .

【 授权许可】

Unknown