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Open AccessArticle

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

1
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
2
Department of Mathematics, Faculty of Technical Science, University Ismail Qemali, 1001 Vlora, Albania
3
Decanato de Ciencias Económicas y Empresariales, Universidad Centroccidental Lisandro Alvarado, Barquisimeto 3001, Venezuela
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2019, 7(11), 1047; https://doi.org/10.3390/math7111047
Received: 28 August 2019 / Revised: 24 September 2019 / Accepted: 27 September 2019 / Published: 3 November 2019
(This article belongs to the Section Mathematics and Computers Science)
In this paper, a quantum trapezium-type inequality using a new class of function, the so-called generalized ϕ -convex function, is presented. A new quantum trapezium-type inequality for the product of two generalized ϕ -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. View Full-Text
Keywords: Hermite–Hadamard inequality; Hölder’s inequality; power mean inequality; quantum estimates; Raina’s function; convex function Hermite–Hadamard inequality; Hölder’s inequality; power mean inequality; quantum estimates; Raina’s function; convex function
MDPI and ACS Style

Vivas-Cortez, M.J.; Liko, R.; Kashuri, A.; Hernández Hernández, J.E. New Quantum Estimates of Trapezium-Type Inequalities for Generalized ϕ-Convex Functions. Mathematics 2019, 7, 1047.

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