On some fractional integral inequalities for generalized strongly modified $h$-convex functions

Peiyu Yan; Qi Li; Yu Ming Chu; Sana Mukhtar; Shumaila Waheed; Peiyu Yan; Qi Li; Yu Ming Chu; Sana Mukhtar; Shumaila Waheed

doi:10.3934/math.2020426

AIMS Mathematics

2020, Volume 5, Issue 6: 6620-6638. doi: 10.3934/math.2020426

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Research article

On some fractional integral inequalities for generalized strongly modified $h$-convex functions

1.
Basic Teaching Department, Shandong Huayu University of Technology, Dezhou, Shandong 253034, China
2.
Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China
3.
Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha 410114, P. R. China
4.
Department of Mathematics, University of Okara, Okara, Pakistan

Received: 11 May 2020 Accepted: 10 August 2020 Published: 25 August 2020
MSC : 26A51, 26A33, 26D15

Convex functions play an important role in many areas of mathematics. They are especially important in the study of optimization problems where they are distinguished by a number of convenient properties. Many generalizations of convex functions exists in literature. The main aim of the article is to develop fractional integral inequalities for generalized strongly modified h-convex functions. Based on obtained fractional type integral inequalities we give some applications to the means. Our results are extension and generalization of many existing results.
- generalized convex functions,
- strongly convex functions,
- modified $h$-convex function
Citation: Peiyu Yan, Qi Li, Yu Ming Chu, Sana Mukhtar, Shumaila Waheed. On some fractional integral inequalities for generalized strongly modified $h$-convex functions[J]. AIMS Mathematics, 2020, 5(6): 6620-6638. doi: 10.3934/math.2020426

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Abstract

Convex functions play an important role in many areas of mathematics. They are especially important in the study of optimization problems where they are distinguished by a number of convenient properties. Many generalizations of convex functions exists in literature. The main aim of the article is to develop fractional integral inequalities for generalized strongly modified h-convex functions. Based on obtained fractional type integral inequalities we give some applications to the means. Our results are extension and generalization of many existing results.

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