Open AccessRefinements of Jensen's inequality and applications
Author(s) -
Tareq Saeed,
AUTHOR_ID,
Muhammad Adil Khan,
Hidayat Ullah,
AUTHOR_ID
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022297
Subject(s) - jensen's inequality , majorization , mathematics , inequality , bhattacharyya distance , inequality of arithmetic and geometric means , convexity , log sum inequality , hölder's inequality , kantorovich inequality , convex function , young's inequality , pure mathematics , entropy (arrow of time) , rearrangement inequality , mathematical economics , discrete mathematics , mathematical analysis , regular polygon , computer science , linear inequality , convex analysis , convex optimization , artificial intelligence , physics , geometry , quantum mechanics , financial economics , economics
The principal aim of this research work is to establish refinements of the integral Jensen's inequality. For the intended refinements, we mainly use the notion of convexity and the concept of majorization. We derive some inequalities for power and quasi–arithmetic means while utilizing the main results. Moreover, we acquire several refinements of Hölder inequality and also an improvement of Hermite–Hadamard inequality as consequences of obtained results. Furthermore, we secure several applications of the acquired results in information theory, which consist bounds for Shannon entropy, different divergences, Bhattacharyya coefficient, triangular discrimination and various distances.