Hadamard and Fejér-Hadamard inequalities for extended generalized fractional integrals involving special functions

Shin Min Kang; Ghulam Farid; Waqas Nazeer; Bushra Tariq

doi:10.1186/s13660-018-1701-3

Hadamard and Fejér-Hadamard inequalities for extended generalized fractional integrals involving special functions

J Inequal Appl. 2018;2018(1):119. doi: 10.1186/s13660-018-1701-3. Epub 2018 May 18.

Authors

Shin Min Kang^{1

2}, Ghulam Farid³, Waqas Nazeer⁴, Bushra Tariq⁵

Affiliations

¹ 1Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University, Jinju, Korea.
² 2Center for General Education, China Medical University, Taichung, Taiwan.
³ Department of Mathematics, COMSATS University, Attock Campus, Pakistan.
⁴ 4Division of Science and Technology, University of Education, Lahore, Pakistan.
⁵ GGPS Kamalpur Alam, Attock, Pakistan.

Abstract

In this paper we prove the Hadamard and the Fejér-Hadamard inequalities for the extended generalized fractional integral operator involving the extended generalized Mittag-Leffler function. The extended generalized Mittag-Leffler function includes many known special functions. We have several such inequalities corresponding to special cases of the extended generalized Mittag-Leffler function. Also there we note the known results that can be obtained.

Keywords: Convex function; Extended generalized Mittag-Leffler function; Fejér–Hadamard inequality; Fractional integrals; Hadamard inequality; m-convex functions.