Refinements of jensen’s and mcshane’s inequalities with applications

In this article, we consider the generalized forms of the Jensen’s inequality given by Jessen and McShane for isotonic linear functionals, derive several refinements for the Jessen’s and McShane’s inequalities connected to certain functions from the linear space, generalize the Jessen’s and McShane’s inequalities pertaining n certain functions. As applications, we provide some improvements for the generalized means, Hölder and generalized Beck’s inequalities. © 2020 the Author(s), licensee AIMS Press.

Authors
Khan M.A.1 , Pečarić J. 2 , Chu Y.-M.3, 4
Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
Number of issue
5
Language
English
Pages
4931-4945
Status
Published
Volume
5
Year
2020
Organizations
  • 1 Department of Mathematics, University of Peshawar, Peshawar, 25000, Pakistan
  • 2 Russian Peoples’ Friendship University, Moscow, 117198, Russian Federation
  • 3 Department of Mathematics, Huzhou University, Huzhou, 313000, China
  • 4 Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha, 410114, China
Keywords
Beck’s inequality; Convex function; Hölder inequality; Jensen’s inequality; Linear functional; McShane’s inequality
Date of creation
02.11.2020
Date of change
02.11.2020
Short link
https://repository.rudn.ru/en/records/article/record/65501/
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