Trapezium-type inequalities for raina’s fractional integrals operator using generalized convex functions

Abstract

first_pagesettings Open AccessArticle Trapezium-Type Inequalities for Raina’s Fractional Integrals Operator Using Generalized Convex Functions by Miguel Vivas-Cortez 1,*,†ORCID,Artion Kashuri 2,†ORCID andJorge E. Hernández Hernández 3,†ORCID 1 Facultad de Ciencias Exactas y Naturales, Pontificia Universidad Católica del Ecuador, Escuela de Matemáticas y Físicas, Quito, Ecuador 2 Department of Mathematics, Faculty of Technical Science, University Ismail Qemali, Vlora, Albania 3 Decanato de Ciencias Económicas y Empresariales, Universidad Centroccidental Lisandro Alvarado, Barquisimeto, Venezuela * Author to whom correspondence should be addressed. † These authors contributed equally to this work. Symmetry 2020, 12(6), 1034; https://doi.org/10.3390/sym12061034 Received: 25 April 2020 / Revised: 6 May 2020 / Accepted: 12 May 2020 / Published: 20 June 2020 Download PDF Citation Export Abstract The authors have reviewed a wide production of scientific articles dealing with the evolution of the concept of convexity and its various applications, and based on this they have detected the relationship that can be established between trapezoidal inequalities, generalized convex functions, and special functions, in particular with the so-called Raina function, which generalizes other better known ones such as the hypergeometric function and the Mittag–Leffler function. The authors approach this situation by studying the Hermite–Hadamard inequality, establishing a useful identity using Raina’s fractional integral operator in the setting of ϕ -convex functions, obtaining some integral inequalities connected with the right-hand side of Hermite–Hadamard-type inequalities for Raina’s fractional integrals. Various special cases have been identified.