Bounds for the Jensen Gap in terms of Power Means with Applications. (29th October 2021)

• Record Type: Journal Article
• Authors: You, Xuexiao; Adil Khan, Muhammad; Moradi, Hamid Reza
• Other Names: Arif Muhammad Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2021(2021)
• Publication Date: 2021-10-29
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2021/1388843
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : 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.