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

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 sp...

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Bibliographic Details
Published in:Symmetry (Basel) 2020-06, Vol.12 (6), p.1034
Main Authors: Vivas-Cortez, Miguel, Kashuri, Artion, Hernández, Jorge E. Hernández
Format: Article
Language:English
Subjects:
Convex analysis
Convexity
generalized convexity
Goal programming
Hermite–Hadamard inequality
Hypergeometric functions
Hölder inequality
Inequalities
Inequality
Integrals
Mathematical functions
Operators (mathematics)
power mean inequality
Raina’s fractional integral operator
Scientific papers
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Summary: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.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym12061034