Some Improvements of Jensen's Inequality via 4-Convexity and Applications. (17th January 2022)

• Record Type: Journal Article
• Authors: Ullah, Hidayat; Adil Khan, Muhammad; Saeed, Tareq; Sayed, Zaid Mohammed Mohammed Mahdi
• Other Names: Malik Sarfraz Nawaz Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2022(2022)
• Publication Date: 2022-01-17
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2022/2157375
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : The intention of this note is to investigate some new important estimates for the Jensen gap while utilizing a 4-convex function. We use the Jensen inequality and definition of convex function in order to achieve the required estimates for the Jensen gap. We acquire new improvements of the Hölder and Hermite–Hadamard inequalities with the help of the main results. We discuss some interesting relations for quasi-arithmetic and power means as consequences of main results. At last, we give the applications of our main inequalities in the information theory. The approach and techniques used in the present note may simulate more research in this field.