A two-point-Padé-approximant-based method for bounding some trigonometric functions

Journal of Inequalities and Applications

Xiao-Diao Chen¹  Yigang Wang¹  Jiapei Jin¹  Junyi Ma¹ 

[1] Key Laboratory of Complex Systems Modeling and Simulation, Hangzhou Dianzi University;

关键词: Wilker’s inequality;    Trigonometric approximation;    Padé approximant;    Two-sided bounds;    Becker–Stark’s inequality;   

DOI  :  10.1186/s13660-018-1726-7

来源: DOAJ

【 摘 要 】

Abstract Inequalities are frequently used for solving practical engineering problem. There are two key issues of bounding inequalities; one is to find the bounds, and the other is to prove the bounds. This paper takes Wilker type inequalities as an example, presents a two-point-Padé-approximant-based method for finding the bounds, and it also provides a method to prove the bounds in a new way. It not only recovers the estimates in Mortici’s method, but it also provides new improvements of estimates obtained from prevailing methods. In principle, it can be applied for other inequalities.

【 授权许可】

Unknown