Derivation of Bounds for Majorization Differences by a Novel Method and Its Applications in Information Theory

被引：3

作者：

Basir, Abdul ^{[1
]}

Khan, Muhammad Adil ^{[1
]}

Ullah, Hidayat ^{[1
]}

Almalki, Yahya ^{[2
]}

Chasreechai, Saowaluck ^{[3
,4
]}

Sitthiwirattham, Thanin ^{[4
,5
]}

机构：

[1] Univ Peshawar, Dept Math, Peshawar 25000, Pakistan

[2] King Khalid Univ, Coll Sci, Dept Math, Abha 61413, Saudi Arabia

[3] King Mongkuts Univ Technol North Bangkok, Fac Appl Sci, Dept Math, Bangkok 10800, Thailand

[4] King Mongkuts Univ Technol North Bangkok, Sci & Technol Res Inst, Res Grp Fract Calculus Theory & Applicat, Bangkok 10800, Thailand

[5] Suan Dusit Univ, Fac Sci & Technol, Math Dept, Bangkok 10300, Thailand

来源：

AXIOMS | 2023年 / 12卷 / 09期

关键词：

convex function; majorization inequality; Slater's inequality; Jensen's inequality; information theory; JENSENS INEQUALITY; CONVEX-FUNCTIONS; REFINEMENTS; COMPANION;

D O I：

10.3390/axioms12090885

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the recent era of research developments, mathematical inequalities and their applications perform a very consequential role in different aspects, and they provide an engaging area for research activities. In this paper, we propose a new approach for the improvement of the classical majorization inequality and its weighted versions in a discrete sense. The proposed improvements give several estimates for the majorization differences. Some earlier improvements of the Jensen and Slater inequalities are deduced as direct consequences of the obtained results. We also discuss the conditions under which the main results give better estimates for the majorization differences. Applications of the acquired results are also presented in information theory.

引用

页数：17

共 59 条

[1]

Abdeljawad T, 2020, ADV DIFFER EQU-NY, V2020, DOI 10.1186/s13662-020-02865-w

[2] Estimation of f-divergence and Shannon entropy by Levin-son type inequalities for higher order convex functions via Taylor polynomial [J].