Some New Results of Mitrinović–Cusa’s and Related Inequalities Based on the Interpolation and Approximation Method
In this paper, new refinements and improvements of Mitrinović–Cusa’s and related inequalities are presented. First, we give new polynomial bounds for sinc(x) and cos(x) functions using the interpolation and approximation method. Based on the obtained results of the above two functions, we establish...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/5595650 |
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| _version_ | 1832550809705906176 |
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| author | Lina Zhang Xuesi Ma |
| author_facet | Lina Zhang Xuesi Ma |
| author_sort | Lina Zhang |
| collection | DOAJ |
| description | In this paper, new refinements and improvements of Mitrinović–Cusa’s and related inequalities are presented. First, we give new polynomial bounds for sinc(x) and cos(x) functions using the interpolation and approximation method. Based on the obtained results of the above two functions, we establish new bounds for Mitrinović–Cusa’s, Wilker’s, Huygens’, Wu–Srivastava’s, and Neuman–Sándor’s inequalities. The analysis results show that our bounds are tighter than the previous methods. |
| format | Article |
| id | doaj-art-013f4e1eca3c4e1e89d600fc310e4fc7 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-013f4e1eca3c4e1e89d600fc310e4fc72025-02-03T06:05:45ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/55956505595650Some New Results of Mitrinović–Cusa’s and Related Inequalities Based on the Interpolation and Approximation MethodLina Zhang0Xuesi Ma1School of Computer Science and Technology, Henan Polytechnic University, Jiaozuo, Henan 454000, ChinaSchool of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, Henan 454000, ChinaIn this paper, new refinements and improvements of Mitrinović–Cusa’s and related inequalities are presented. First, we give new polynomial bounds for sinc(x) and cos(x) functions using the interpolation and approximation method. Based on the obtained results of the above two functions, we establish new bounds for Mitrinović–Cusa’s, Wilker’s, Huygens’, Wu–Srivastava’s, and Neuman–Sándor’s inequalities. The analysis results show that our bounds are tighter than the previous methods.http://dx.doi.org/10.1155/2021/5595650 |
| spellingShingle | Lina Zhang Xuesi Ma Some New Results of Mitrinović–Cusa’s and Related Inequalities Based on the Interpolation and Approximation Method Journal of Mathematics |
| title | Some New Results of Mitrinović–Cusa’s and Related Inequalities Based on the Interpolation and Approximation Method |
| title_full | Some New Results of Mitrinović–Cusa’s and Related Inequalities Based on the Interpolation and Approximation Method |
| title_fullStr | Some New Results of Mitrinović–Cusa’s and Related Inequalities Based on the Interpolation and Approximation Method |
| title_full_unstemmed | Some New Results of Mitrinović–Cusa’s and Related Inequalities Based on the Interpolation and Approximation Method |
| title_short | Some New Results of Mitrinović–Cusa’s and Related Inequalities Based on the Interpolation and Approximation Method |
| title_sort | some new results of mitrinovic cusa s and related inequalities based on the interpolation and approximation method |
| url | http://dx.doi.org/10.1155/2021/5595650 |
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