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

• Main Authors: Xiaoli Qiang, Ghulam Farid, Muhammad Yussouf, Khuram Ali Khan, Atiq Ur Rahman
• Format: Article
• Language: English
• Published: SpringerOpen 2020-07-01
• Series: Journal of Inequalities and Applications
• Subjects: Harmonically convex function; Hadamard inequality; Fejér–Hadamard inequality; Mittag-Leffler function; Fractional integral operators
• Online Access: http://link.springer.com/article/10.1186/s13660-020-02457-y
• ISSN: 1029-242X

Abstract 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.