Refinements of Jensen’s and McShane’s inequalities with applications

Muhammad Adil Khan; Josip Pečarić; Yu-Ming Chu; Muhammad Adil Khan; Josip Pečarić; Yu-Ming Chu

doi:10.3934/math.2020315

AIMS Mathematics

2020, Volume 5, Issue 5: 4931-4945. doi: 10.3934/math.2020315

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Research article

Refinements of Jensen’s and McShane’s inequalities with applications

1.
Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan
2.
Russian Peoples’ Friendship University, 117198 Moscow, Russia
3.
Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China
4.
Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha 410114, P. R. China

Received: 29 March 2020 Accepted: 27 May 2020 Published: 04 June 2020
MSC : 26B25, 26D15

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, Holder and generalized Beck's inequalities.
- Jensen’s inequality,
- convex function,
- linear functional,
- McShane’s inequality,
- Hölder inequality,
- Beck’s inequality
Citation: Muhammad Adil Khan, Josip Pečarić, Yu-Ming Chu. Refinements of Jensen’s and McShane’s inequalities with applications[J]. AIMS Mathematics, 2020, 5(5): 4931-4945. doi: 10.3934/math.2020315

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Abstract

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, Holder and generalized Beck's inequalities.

References

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