On Hermite-Hadamard type inequalities for $ n $-polynomial convex stochastic processes

Haoliang Fu; Muhammad Shoaib Saleem; Waqas Nazeer; Mamoona Ghafoor; Peigen Li; Haoliang Fu; Muhammad Shoaib Saleem; Waqas Nazeer; Mamoona Ghafoor; Peigen Li

doi:10.3934/math.2021371

AIMS Mathematics

2021, Volume 6, Issue 6: 6322-6339. doi: 10.3934/math.2021371

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Research article

On Hermite-Hadamard type inequalities for $ n $-polynomial convex stochastic processes

1.
School of Finance, Guangdong University of Finance and Economics, Guangzhou 510320, China
2.
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
3.
Department of Mathematics, University of Okara, Okara Pakistan
4.
Department of Mathematics, GC University, Lahore Pakistan

Received: 03 January 2021 Accepted: 22 March 2021 Published: 12 April 2021
MSC : 34N05, 35A23

In this note, our purpose is to introduce the concept of $ n $-polynomial convex stochastic processes and study some of their algebraic properties. We establish new refinements for integral version of Hölder and power mean inequality. Also, we are concerned to extend several Hermite-Hadamard type inequalities for $ n $-polynomial convex stochastic processes by using Hölder, Hölder-İşcan, power mean and improved power mean integral inequalities. Moreover, we give comparison of obtained results.
- convex stochastic process,
- $ n $-polynomial,
- Hölder-İşcan integral inequality,
- Hermite-Hadamard inequality
Citation: Haoliang Fu, Muhammad Shoaib Saleem, Waqas Nazeer, Mamoona Ghafoor, Peigen Li. On Hermite-Hadamard type inequalities for $ n $-polynomial convex stochastic processes[J]. AIMS Mathematics, 2021, 6(6): 6322-6339. doi: 10.3934/math.2021371

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Abstract

In this note, our purpose is to introduce the concept of $ n $-polynomial convex stochastic processes and study some of their algebraic properties. We establish new refinements for integral version of Hölder and power mean inequality. Also, we are concerned to extend several Hermite-Hadamard type inequalities for $ n $-polynomial convex stochastic processes by using Hölder, Hölder-İşcan, power mean and improved power mean integral inequalities. Moreover, we give comparison of obtained results.

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