Several Double Inequalities for Integer Powers of the Sinc and Sinhc Functions with Applications to the Neuman–Sándor Mean and the First Seiffert Mean
In the paper, the authors establish a general inequality for the hyperbolic functions, extend the newly-established inequality to trigonometric functions, obtain some new inequalities involving the inverse sine and inverse hyperbolic sine functions, and apply these inequalities to the Neuman–Sándor...
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-06-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/7/304 |
| _version_ | 1797407453947625472 |
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| author | Wen-Hui Li Qi-Xia Shen Bai-Ni Guo |
| author_facet | Wen-Hui Li Qi-Xia Shen Bai-Ni Guo |
| author_sort | Wen-Hui Li |
| collection | DOAJ |
| description | In the paper, the authors establish a general inequality for the hyperbolic functions, extend the newly-established inequality to trigonometric functions, obtain some new inequalities involving the inverse sine and inverse hyperbolic sine functions, and apply these inequalities to the Neuman–Sándor mean and the first Seiffert mean. |
| first_indexed | 2024-03-09T03:42:44Z |
| format | Article |
| id | doaj.art-b24fed161a694b118db555101fb5ec53 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T03:42:44Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-b24fed161a694b118db555101fb5ec532023-12-03T14:39:11ZengMDPI AGAxioms2075-16802022-06-0111730410.3390/axioms11070304Several Double Inequalities for Integer Powers of the Sinc and Sinhc Functions with Applications to the Neuman–Sándor Mean and the First Seiffert MeanWen-Hui Li0Qi-Xia Shen1Bai-Ni Guo2Department of Basic Courses, Zhengzhou University of Science and Technology, Zhengzhou 450064, ChinaDepartment of Basic Courses, Zhengzhou University of Science and Technology, Zhengzhou 450064, ChinaSchool of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454010, ChinaIn the paper, the authors establish a general inequality for the hyperbolic functions, extend the newly-established inequality to trigonometric functions, obtain some new inequalities involving the inverse sine and inverse hyperbolic sine functions, and apply these inequalities to the Neuman–Sándor mean and the first Seiffert mean.https://www.mdpi.com/2075-1680/11/7/304Neuman–Sándor meanSeiffert meaninequalitysinc functionsinhc functioninverse hyperbolic function |
| spellingShingle | Wen-Hui Li Qi-Xia Shen Bai-Ni Guo Several Double Inequalities for Integer Powers of the Sinc and Sinhc Functions with Applications to the Neuman–Sándor Mean and the First Seiffert Mean Axioms Neuman–Sándor mean Seiffert mean inequality sinc function sinhc function inverse hyperbolic function |
| title | Several Double Inequalities for Integer Powers of the Sinc and Sinhc Functions with Applications to the Neuman–Sándor Mean and the First Seiffert Mean |
| title_full | Several Double Inequalities for Integer Powers of the Sinc and Sinhc Functions with Applications to the Neuman–Sándor Mean and the First Seiffert Mean |
| title_fullStr | Several Double Inequalities for Integer Powers of the Sinc and Sinhc Functions with Applications to the Neuman–Sándor Mean and the First Seiffert Mean |
| title_full_unstemmed | Several Double Inequalities for Integer Powers of the Sinc and Sinhc Functions with Applications to the Neuman–Sándor Mean and the First Seiffert Mean |
| title_short | Several Double Inequalities for Integer Powers of the Sinc and Sinhc Functions with Applications to the Neuman–Sándor Mean and the First Seiffert Mean |
| title_sort | several double inequalities for integer powers of the sinc and sinhc functions with applications to the neuman sandor mean and the first seiffert mean |
| topic | Neuman–Sándor mean Seiffert mean inequality sinc function sinhc function inverse hyperbolic function |
| url | https://www.mdpi.com/2075-1680/11/7/304 |
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