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New bounds of Wilker- and Huygens-type inequalities for inverse trigonometric functions

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

By using two-parameter functions, this paper presents a family of new Wilker and Huygens type inequalities involving inverse trigonometric functions. It can recover parts of previous results, and can also achieve much better approximation performance than those of prevailing methods. The application of approximating the integral computation is shown by numerical examples, which shows the better approximation effect of the new method. More other forms of bounding functions, or even three-parameter functions, can be used for further improvement.

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Acknowledgements

This research work was partially supported by Zhejiang Key Research and Development Project of China (LY19F020041, 2018C01030), the National Natural Science Foundation of China (61972120, 61672009).

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Authors and Affiliations

  1. Key Laboratory of Complex Systems Modeling and Simulation, Hangzhou Dianzi University, Hangzhou, China

    Xiao-Diao Chen

  2. School of Computer, Hangzhou Dianzi University, Hangzhou, China

    Hui Wang & Kang Yang

  3. School of Artificial Intelligence and Big Data, Hefei University, Hefei, China

    Jin Xie

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  1. Xiao-Diao Chen
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  2. Hui Wang
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  4. Jin Xie
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Correspondence to Xiao-Diao Chen.

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Chen, XD., Wang, H., Yang, K. et al. New bounds of Wilker- and Huygens-type inequalities for inverse trigonometric functions. RACSAM 115, 36 (2021). https://doi.org/10.1007/s13398-020-00969-2

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