Fractional integral versions of Hermite-Hadamard type inequality for generalized exponentially convexity

AIMS Mathematics

Hengxiao Qi¹  Muhammad Yussouf²  Sajid Mehmood³  Yu-Ming Chu⁴  Ghulam Farid⁵ 

[1] 1 Party School of Shandong Provincial Committee of the Communist Party of China (Shandong Administration College), Jinan 250014, China;2 Department of Mathematics, University of Sargodha, Sargodha, Pakistan;3 Govt Boys Primary school Sherani, Hazro, Attock, Pakistan;4 Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China 5 Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha 410114, P. R. China;6 Department of Mathematics, COMSATS University Islamabad, Attock Campus, Pakistan;

关键词: convex function;    hermite-hadamard inequality;    generalized fractional integral operators;    mittag-leffler function;   

DOI  :  10.3934/math.2020386

来源: DOAJ

【 摘 要 】

In this paper, we establish generalized fractional versions of Hermite-Hadamard inequalities for exponentially (α, h − m)-convex functions, exponentially (h − m)-convex functions and exponentially (α, m)-convex functions. These inequalities arise when using the generalized fractional integral operators containing Mittag-Leffler function via a monotonically increasing function. The presented results hold at the same time for various kinds of convexities and well-known fractional integral operators. Moreover, the established inequalities reproduce several known results which are part of the existing literature.

【 授权许可】

Unknown