Properties and Bounds of Jensen-Type Functionals via Harmonic Convex Functions. (9th August 2021)

• Record Type: Journal Article
• Authors: Mughal, Aqeel Ahmad; Almusawa, Hassan; Haq, Absar Ul; Baloch, Imran Abbas
• Other Names: Akdemir Ahmet Ocak Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2021(2021)
• Publication Date: 2021-08-09
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2021/5561611
• Languages: English
• ISSNs: 2314-4629

Abstract

Abstract : Dragomir introduced the Jensen-type inequality for harmonic convex functions (HCF) and Baloch et al. studied its different variants, such as Jensen-type inequality for harmonic h -convex functions. In this paper, we aim to establish the functional form of inequalities presented by Baloch et al. and prove the superadditivity and monotonicity properties of these functionals. Furthermore, we derive the bound for these functionals under certain conditions. Furthermore, we define more generalized functionals involving monotonic nondecreasing concave function as well as evince superadditivity and monotonicity properties of these generalized functionals.