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Some Wilker and Cusa type inequalities for generalized trigonometric and hyperbolic functions
Li-Guo Huang1, Li Yin1, Yong-Li Wang2
11College of Science, Binzhou University, Binzhou, China.
Journal of Inequalities and Applications
|March 13, 2018
Summary
Researchers derived new Wilker and Cusa-type inequalities for generalized trigonometric and hyperbolic functions. These findings extend and refine existing mathematical inequalities in analysis.
Area of Science:
- Mathematical Analysis
- Inequalities
- Trigonometric Functions
- Hyperbolic Functions
Background:
- Wilker and Cusa inequalities are fundamental in mathematical analysis.
- Generalizations of trigonometric and hyperbolic functions are crucial for extending mathematical theories.
- Existing inequalities may not cover all generalized function cases.
Purpose of the Study:
- To establish novel Wilker-type inequalities.
- To derive new Cusa-type inequalities.
- To generalize known inequalities for trigonometric and hyperbolic functions.
Main Methods:
- Utilizing analytical techniques to derive inequalities.
- Applying properties of generalized trigonometric and hyperbolic functions.
- Comparing derived inequalities with existing ones.
Main Results:
- New Wilker-type inequalities were obtained for generalized functions.
- New Cusa-type inequalities were established for generalized functions.
- Several known inequalities were successfully generalized.
Conclusions:
- The study successfully extends Wilker and Cusa type inequalities.
- The findings provide a broader framework for analyzing generalized trigonometric and hyperbolic functions.
- This work contributes to the theory of mathematical inequalities.
Keywords:
Arithmetic–geometric means inequalityCusa type inequalityGeneralized hyperbolic functionGeneralized trigonometric functionPower means inequalityWilker type inequalityMore Related Videos
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