Refining the integral Jensen inequality for finite signed measures using majorization

Author:

Horváth LászlóORCID

Abstract

AbstractAmong inequalities that use the concept of convexity, Jensen-type inequalities and majorization-type inequalities are significant and fundamental. An important and widely researched area in the study of Jensen-type inequalities is the refinement of such inequalities. In this paper, we provide a general method for refining the integral Jensen inequality for finite signed measures using integral majorization inequalities. Under the conditions considered in the paper, the results are unique, and even for measures, they give a new approach. We also provide interesting specific refinements, some of which relate to Jensen–Steffensen’s inequality. A new and extended version of this inequality is also obtained in the paper.

Funder

Hungarian National Research, Development and Innovation Office

Publisher

Springer Science and Business Media LLC

Reference18 articles.

1. Bakula, M.K., Matić, M., Pečarić, J.: Generalizations of the Jensen–Steffensen and related inequalities. Cent. Eur. J. Math. 7(4), 787–803 (2009)

2. Barnett, N.S., Cerone, P., Dragomir, S.S.: Majorisation inequalities for Stieltjes integrals. Appl. Math. Lett. 22, 416–421 (2009)

3. Boas, R.P.: The Jensen–Steffensen inequality. Publ. Elektroteh. Fak. Univ. Beogr. Ser. Mat. 302(319), 1–8 (1970)

4. Deng, Y., Ullah, H., Khan, M.A., Iqbal, S., Wu, S.: Refinements of Jensen’s inequality via majorization results with applications in the information theory. J. Math. 2021, 1951799, 12 pages (2021)

5. Fink, A.M.: A best possible Hadamard inequality. Math. Inequal. Appl. 1, 223–230 (1998)

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3