New Quantum Estimates of Trapezium-Type Inequalities for Generalized ϕ-Convex Functions
by
Miguel J. Vivas-Cortez 1,*,†
, Rozana Liko 2,†, Artion Kashuri 2,† and Jorge E. Hernández Hernández 3,†
Miguel J. Vivas-Cortez 1,*,†, Rozana Liko 2,†, Artion Kashuri 2,† and Jorge E. Hernández Hernández 3,†
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 -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 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.
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Keywords:
Hermite–Hadamard inequality; Hölder’s inequality; power mean inequality; quantum estimates; Raina’s function; convex function
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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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