Uniform Treatment of Jensen’s Inequality by Montgomery Identity
We generalize Jensen’s integral inequality for real Stieltjes measure by using Montgomery identity under the effect of n−convex functions; also, we give different versions of Jensen’s discrete inequality along with its converses for real weights. As an application, we give generalized variants of He...
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| Main Authors: | , , , , |
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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/10.1155/2021/5564647 |
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| _version_ | 1832554000741826560 |
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| author | Tahir Rasheed Saad Ihsan Butt Đilda Pečarić Josip Pečarić Ahmet Ocak Akdemir |
| author_facet | Tahir Rasheed Saad Ihsan Butt Đilda Pečarić Josip Pečarić Ahmet Ocak Akdemir |
| author_sort | Tahir Rasheed |
| collection | DOAJ |
| description | We generalize Jensen’s integral inequality for real Stieltjes measure by using Montgomery identity under the effect of n−convex functions; also, we give different versions of Jensen’s discrete inequality along with its converses for real weights. As an application, we give generalized variants of Hermite–Hadamard inequality. Montgomery identity has a great importance as many inequalities can be obtained from Montgomery identity in q−calculus and fractional integrals. Also, we give applications in information theory for our obtained results, especially for Zipf and Hybrid Zipf–Mandelbrot entropies. |
| format | Article |
| id | doaj-art-326da00a639440cf80105a12b997bf2f |
| 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-326da00a639440cf80105a12b997bf2f2025-02-03T05:52:38ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/55646475564647Uniform Treatment of Jensen’s Inequality by Montgomery IdentityTahir Rasheed0Saad Ihsan Butt1Đilda Pečarić2Josip Pečarić3Ahmet Ocak Akdemir4COMSATS University Islamabad, Lahore Campus, Lahore, PakistanCOMSATS University Islamabad, Lahore Campus, Lahore, PakistanDepartment of Media and Communication, University North, Trg dr. Žarka Dolinara 1, Koprivnica, CroatiaPeoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow 117198, RussiaDepartment of Mathematics, Faculty of Arts and Sciences, A ğrı İbrahim Çeçen University, Ağrı, TurkeyWe generalize Jensen’s integral inequality for real Stieltjes measure by using Montgomery identity under the effect of n−convex functions; also, we give different versions of Jensen’s discrete inequality along with its converses for real weights. As an application, we give generalized variants of Hermite–Hadamard inequality. Montgomery identity has a great importance as many inequalities can be obtained from Montgomery identity in q−calculus and fractional integrals. Also, we give applications in information theory for our obtained results, especially for Zipf and Hybrid Zipf–Mandelbrot entropies.http://dx.doi.org/10.1155/2021/5564647 |
| spellingShingle | Tahir Rasheed Saad Ihsan Butt Đilda Pečarić Josip Pečarić Ahmet Ocak Akdemir Uniform Treatment of Jensen’s Inequality by Montgomery Identity Journal of Mathematics |
| title | Uniform Treatment of Jensen’s Inequality by Montgomery Identity |
| title_full | Uniform Treatment of Jensen’s Inequality by Montgomery Identity |
| title_fullStr | Uniform Treatment of Jensen’s Inequality by Montgomery Identity |
| title_full_unstemmed | Uniform Treatment of Jensen’s Inequality by Montgomery Identity |
| title_short | Uniform Treatment of Jensen’s Inequality by Montgomery Identity |
| title_sort | uniform treatment of jensen s inequality by montgomery identity |
| url | http://dx.doi.org/10.1155/2021/5564647 |
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