Bounds for the Jensen Gap in terms of Power Means with Applications
Jensen’s and its related inequalities have attracted the attention of several mathematicians due to the fact that Jensen’s inequality has numerous applications in almost all disciplines of mathematics and in other fields of science. In this article, we propose new bounds for the difference of two si...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/1388843 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832547646957420544 |
|---|---|
| author | Xuexiao You Muhammad Adil Khan Hamid Reza Moradi |
| author_facet | Xuexiao You Muhammad Adil Khan Hamid Reza Moradi |
| author_sort | Xuexiao You |
| collection | DOAJ |
| description | Jensen’s and its related inequalities have attracted the attention of several mathematicians due to the fact that Jensen’s inequality has numerous applications in almost all disciplines of mathematics and in other fields of science. In this article, we propose new bounds for the difference of two sides of Jensen’s inequality in terms of power means. An example has been presented for the importance and support of the main results. Related results have been given in quantum calculus. As consequences, improvements of quantum integral version of Hermite-Hadamard inequality have been derived. The obtained inequalities have been applied for some well-known inequalities such as Hermite-Hadamrd, Hölder, and power mean inequalities. Finally, some applications are given in information theory. The tools performed for obtaining the main results may be applied to obtain more results for other inequalities. |
| format | Article |
| id | doaj-art-7870763a1cb74deaa3348ee7b92d0f30 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-7870763a1cb74deaa3348ee7b92d0f302025-02-03T06:43:54ZengWileyJournal of Function Spaces2314-88882021-01-01202110.1155/2021/1388843Bounds for the Jensen Gap in terms of Power Means with ApplicationsXuexiao You0Muhammad Adil Khan1Hamid Reza Moradi2School of Mathematics and StatisticsDepartment of MathematicsDepartment of MathematicsJensen’s and its related inequalities have attracted the attention of several mathematicians due to the fact that Jensen’s inequality has numerous applications in almost all disciplines of mathematics and in other fields of science. In this article, we propose new bounds for the difference of two sides of Jensen’s inequality in terms of power means. An example has been presented for the importance and support of the main results. Related results have been given in quantum calculus. As consequences, improvements of quantum integral version of Hermite-Hadamard inequality have been derived. The obtained inequalities have been applied for some well-known inequalities such as Hermite-Hadamrd, Hölder, and power mean inequalities. Finally, some applications are given in information theory. The tools performed for obtaining the main results may be applied to obtain more results for other inequalities.http://dx.doi.org/10.1155/2021/1388843 |
| spellingShingle | Xuexiao You Muhammad Adil Khan Hamid Reza Moradi Bounds for the Jensen Gap in terms of Power Means with Applications Journal of Function Spaces |
| title | Bounds for the Jensen Gap in terms of Power Means with Applications |
| title_full | Bounds for the Jensen Gap in terms of Power Means with Applications |
| title_fullStr | Bounds for the Jensen Gap in terms of Power Means with Applications |
| title_full_unstemmed | Bounds for the Jensen Gap in terms of Power Means with Applications |
| title_short | Bounds for the Jensen Gap in terms of Power Means with Applications |
| title_sort | bounds for the jensen gap in terms of power means with applications |
| url | http://dx.doi.org/10.1155/2021/1388843 |
| work_keys_str_mv | AT xuexiaoyou boundsforthejensengapintermsofpowermeanswithapplications AT muhammadadilkhan boundsforthejensengapintermsofpowermeanswithapplications AT hamidrezamoradi boundsforthejensengapintermsofpowermeanswithapplications |