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Open AccessArticle

Some Inequalities Using Generalized Convex Functions in Quantum Analysis

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Escuela de Ciencias Físicas y Matemáticas, Facultad de Ciencias Exactas y Naturales, Pontificia Universidad Católica del Ecuador, Av. 12 de Octubre 1076. Apartado, Quito 17-01-2184, Ecuador
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Department of Mathematics, Faculty of Technical Science, University Ismail Qemali, L. Pavaresia, Vlora 1001, Vlore, Albania
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Departamento de Técnicas Cuantitativas, Decanato de Ciencias Económicas y Empresariales, Universidad Centroccidental Lisandro Alvarado, Av. 20. esq. Av. Moran, Edf. Los Militares, Piso 2, Ofc.2, Barquisimeto 3001, Venezuela
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Author to whom correspondence should be addressed.
Symmetry 2019, 11(11), 1402; https://doi.org/10.3390/sym11111402
Received: 23 September 2019 / Revised: 16 October 2019 / Accepted: 17 October 2019 / Published: 13 November 2019
In the present work, the Hermite–Hadamard inequality is established in the setting of quantum calculus for a generalized class of convex functions depending on three parameters: a number in ( 0 , 1 ] and two arbitrary real functions defined on [ 0 , 1 ] . From the proven results, various inequalities of the same type are deduced for other types of generalized convex functions and the methodology used reveals, in a sense, a symmetric mathematical phenomenon. In addition, the definition of dominated convex functions with respect to the generalized class of convex functions aforementioned is introduced, and some integral inequalities are established. View Full-Text
Keywords: integral inequalities; (m,h1,h2)-convex functions; dominated convexity; quantum calculus integral inequalities; (m,h1,h2)-convex functions; dominated convexity; quantum calculus
MDPI and ACS Style

Vivas-Cortez, M.J.; Kashuri, A.; Liko, R.; Hernández, J.E.H. Some Inequalities Using Generalized Convex Functions in Quantum Analysis. Symmetry 2019, 11, 1402.

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