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Open AccessArticle

Trapezium-Type Inequalities for Raina’s Fractional Integrals Operator Using Generalized Convex Functions

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
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. View Full-Text
Keywords: Hermite–Hadamard inequality; Raina’s fractional integral operator; Hölder inequality; power mean inequality; generalized convexity Hermite–Hadamard inequality; Raina’s fractional integral operator; Hölder inequality; power mean inequality; generalized convexity
MDPI and ACS Style

Vivas-Cortez, M.; Kashuri, A.; Hernández, J.E.H. Trapezium-Type Inequalities for Raina’s Fractional Integrals Operator Using Generalized Convex Functions. Symmetry 2020, 12, 1034.

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