New Quantum Estimates of Trapezium-Type Inequalities for Generalized ? -Convex Functions

Miguel J. Vivas-Cortez, Rozana Liko, Artion Kashuri and Jorge E. Hernández Hernández
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Miguel J. Vivas-Cortez: Facultad de Ciencias Exactas y Naturales, Escuela de Matemáticas y Físicas, Pontificia Universidad Católica del Ecuador, Av. 12 de Octubre 1076. Apartado: 17-01-2184, Quito 170143, Ecuador
Rozana Liko: Department of Mathematics, Faculty of Technical Science, University Ismail Qemali, 1001 Vlora, Albania
Artion Kashuri: Department of Mathematics, Faculty of Technical Science, University Ismail Qemali, 1001 Vlora, Albania
Jorge E. Hernández Hernández: Decanato de Ciencias Económicas y Empresariales, Universidad Centroccidental Lisandro Alvarado, Barquisimeto 3001, Venezuela

Mathematics, 2019, vol. 7, issue 11, 1-19

Abstract: In this paper, a quantum trapezium-type inequality using a new class of function, the so-called generalized ? -convex function, is presented. A new quantum trapezium-type inequality for the product of two generalized ? -convex functions is provided. The authors also prove an identity for twice q - differentiable functions using Raina’s function. Utilizing the identity established, certain quantum estimated inequalities for the above class are developed. Various special cases have been studied. A brief conclusion is also given.

Keywords: Hermite–Hadamard inequality; Hölder’s inequality; power mean inequality; quantum estimates; Raina’s function; convex function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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