A weighted and exponential generalization of Wilker's inequality and its applications

Abstract

In this paper, the authors first prove a weighted and exponential generalization of Wilker's inequality. The main result presented here is then applied with a view to deriving an improved version of the Sándor–Bencze conjectured inequality. Some other closely-related inequalities are also considered.

Keywords:

• Wilker's inequality
• Huygens's inequality
• Weighted generalization
• Sándor–Bencze conjectured inequality
• Weighted inequalities
• Exponential generalization

Acknowledgements

The present investigation was supported, in part, by the Natural Science Foundation of the Fujian Province of the People's Republic of China under Grant 2006J0197 and, in part, by the Natural Sciences and Engineering Research Council of Canada under Grant OGP0007353.