Inequalities for the generalized trigonometric and hyperbolic functions

By R. Kl'en, Matti Vuorinen, Xiaohui Zhang. 2012

56 citations recorded by the source corpus.

The generalized trigonometric functions occur as an eigenfunction of the Dirichlet problem for the one-dimensional $p-$Laplacian. The generalized hyperbolic functions are defined similarly. Some classical inequalities for trigonometric and hyperbolic functions, such as Mitrinovi\'c-Adamovi\'c inequality, Lazarevi\'c's inequality, Huygens-type inequalities, Wilker-type inequalities, and Cuza-Huygens-type inequalities, are generalized to the case of generalized functions.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/c86d8d0dd8a89e835ba26541aea185028d94e34d

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In Applied Mathematics

1. Y. Chu
2. Miao-Kun Wang
3. Zhonghua Shen
4. Miao-Ying Hong
5. Yangfan Xu
6. Tie-hong Zhao
7. Wei-Mao Qian
8. Zhen-Hang Yang

Citations in the corpus

• Inequalities for generalized trigonometric and hyperbolic functions with one parameter (2020, background): “In particular, a lot of well known properties and inequalities for the classical trigonometric functions had been generalized to these cases [10, 11, 44].”