Further generalizations of Hadamard and Fejér–Hadamard fractional inequalities and error estimates

Advances in Difference Equations

article

Rao, Yongsheng¹  Yussouf, Muhammad²  Farid, Ghulam³  Pečarić, Josip⁴  Tlili, Iskander⁵ 

[1] Institute of Computing Science and Technology, Guangzhou University;Department of Mathematics, University of Sargodha;Department of Mathematics, COMSATS University Islamabad;Rudn University;Institute of Research and Development, Duy Tan University;Faculty of Civil Engineering, Duy Tan University

关键词: Convex functions;    Hadamard inequality;    Generalized fractional integrals;    Mittag-Leffler function;   

DOI  :  10.1186/s13662-020-02872-x

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

The aim of this paper is to generalize the fractional Hadamard and Fejér–Hadamard inequalities. By using a generalized fractional integral operator containing extended Mittag-Leffler function via monotone function, for convex functions we generalize well known fractional Hadamard and Fejér–Hadamard inequalities. Also we study the error bounds of these generalized Hadamard and Fejér–Hadamard inequalities. We also obtain some published results from presented inequalities.

【 授权许可】

CC BY