Sharpening and generalizations of Shafer's inequality for the arc sine function

Abstract

In this paper, by a concise and elementary approach, we sharpen and generalize Shafer's inequality for the arc sine function, and some known results are extended and generalized.

Keywords:

• sharpening
• generalization
• Shafer's inequality
• arc sine function
• monotonicity

2000 Mathematics Subject Classification :

• Primary: 33B10
• Secondary: 26D05

Acknowledgements

The authors were partially supported by the China Scholarship Council and the Science Foundation of Tianjin Polytechnic University. The authors would like to express their appreciation for the anonymous referees, for their helpful suggestions to and valuable comments on this manuscript.