New generalized fractional versions of Hadamard and Fejér inequalities for harmonically convex functions

Journal of inequalities and applications

article

Xiaoli Qiang¹  Ghulam Farid²  Muhammad Yussouf³  Khuram Ali Khan³  Atiq Ur Rahman² 

[1] Institute of Computing Science and Technology, Guangzhou University;Department of Mathematics, COMSATS University Islamabad, Attock Campus;Department of Mathematics, University of Sargodha

关键词: Harmonically convex function;    Hadamard inequality;    Fejér–Hadamard inequality;    Mittag-Leffler function;    Fractional integral operators;   

DOI  :  10.1186/s13660-020-02457-y

学科分类：电力

来源: SpringerOpen

【 摘 要 】

The aim of this paper is to establish new generalized fractional versions of the Hadamard and the Fejér–Hadamard integral inequalities for harmonically convex functions. Fractional integral operators involving an extended generalized Mittag-Leffler function which are further generalized via a monotone increasing function are utilized to get these generalized fractional versions. The results of this paper give several consequent fractional inequalities for harmonically convex functions for known fractional integral operators deducible from utilized generalized fractional integral operators.

【 授权许可】

CC BY