Hermite-Hadamard and Jensen’s type inequalities for modified (<em>p, h</em>)-convex functions

Baoli Feng; Mamoona Ghafoor; Yu Ming Chu; Muhammad Imran Qureshi; Xue Feng; Chuang Yao; Xing Qiao; Baoli Feng; Mamoona Ghafoor; Yu Ming Chu; Muhammad Imran Qureshi; Xue Feng; Chuang Yao; Xing Qiao

doi:10.3934/math.2020446

AIMS Mathematics

2020, Volume 5, Issue 6: 6959-6971. doi: 10.3934/math.2020446

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Research article

Hermite-Hadamard and Jensen’s type inequalities for modified (p, h)-convex functions

1.
Mudanjiang Normal University, Mudanjiang City, 157011, China
2.
Department of Mathematics, University of Okara, Okara Pakistan
3.
Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China
4.
Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering,
5.
Department of Mathematics, COMSATS University Islamabad, Vehari Campus, Vehari Pakistan
6.
Aviation University Air Force, Changchun City, 1300000, Chinan
7.
Heilongjiang bayi agricultural reclamation university Daqing City, 158308, China
8.
Department of Mathematics, Daqing Normal University, Daqing City, 163712, China

Received: 01 July 2020 Accepted: 19 August 2020 Published: 08 September 2020
MSC : 26A51, 26A33, 26D15

In this study, we will derive the conception of modified (p, h)-convex functions which will unify p-convexity with modified h-convexity. We will investigate the fundamental properties of modified (p, h)-convexity. Furthermore, we will derive the Hermite-Hadamard, Fejér and Jensen's type inequalities for this generalization.
- p-convex function,
- modified h-convex function,
- Hermite-Hadamard inequality,
- Fejér type inequalities,
- Jensen’s type inequalities
Citation: Baoli Feng, Mamoona Ghafoor, Yu Ming Chu, Muhammad Imran Qureshi, Xue Feng, Chuang Yao, Xing Qiao. Hermite-Hadamard and Jensen’s type inequalities for modified (p, h)-convex functions[J]. AIMS Mathematics, 2020, 5(6): 6959-6971. doi: 10.3934/math.2020446

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Abstract

In this study, we will derive the conception of modified (p, h)-convex functions which will unify p-convexity with modified h-convexity. We will investigate the fundamental properties of modified (p, h)-convexity. Furthermore, we will derive the Hermite-Hadamard, Fejér and Jensen's type inequalities for this generalization.

References

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