q-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions

q-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions

In this paper, we prove the correct q-Hermite–Hadamard inequality, some new q-Hermite–Hadamard inequalities, and generalized q-Hermite–Hadamard inequality. By using the left hand part of the correct q-Hermite–Hadamard inequality, we have a new equality. Finally using the new equality, we give some q...

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Main Authors: Necmettin Alp, Mehmet Zeki Sarıkaya, Mehmet Kunt, İmdat İşcan
Format: Article
Language:English
Published: Elsevier 2018-04-01
Series:Journal of King Saud University: Science
Online Access:http://www.sciencedirect.com/science/article/pii/S1018364716304839
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spelling doaj-b5e4bc45f406499585145ffbc2847b932020-11-24T22:26:45ZengElsevierJournal of King Saud University: Science1018-36472018-04-01302193203q-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functionsNecmettin Alp0Mehmet Zeki Sarıkaya1Mehmet Kunt2İmdat İşcan3Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, TurkeyDepartment of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, TurkeyDepartment of Mathematics, Faculty of Sciences, Karadeniz Technical University, 61080 Trabzon, Turkey; Corresponding author at: Department of Mathematics, Faculty of Sciences, Karadeniz Technical University, 61080 Trabzon, Turkey.Department of Mathematics, Faculty of Sciences and Arts, Giresun University, 28200 Giresun, TurkeyIn this paper, we prove the correct q-Hermite–Hadamard inequality, some new q-Hermite–Hadamard inequalities, and generalized q-Hermite–Hadamard inequality. By using the left hand part of the correct q-Hermite–Hadamard inequality, we have a new equality. Finally using the new equality, we give some q-midpoint type integral inequalities through q-differentiable convex and q-differentiable quasi-convex functions. Many results given in this paper provide extensions of others given in previous works. Keywords: Hermite–Hadamard inequality, Midpoint type inequality, q-Integral inequalities, q-Derivative, q-Integration, Convexity, Quasi-convexityhttp://www.sciencedirect.com/science/article/pii/S1018364716304839
collection DOAJ
language English
format Article
sources DOAJ
author Necmettin Alp
Mehmet Zeki Sarıkaya
Mehmet Kunt
İmdat İşcan
spellingShingle Necmettin Alp
Mehmet Zeki Sarıkaya
Mehmet Kunt
İmdat İşcan
q-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions
Journal of King Saud University: Science
author_facet Necmettin Alp
Mehmet Zeki Sarıkaya
Mehmet Kunt
İmdat İşcan
author_sort Necmettin Alp
title q-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions
title_short q-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions
title_full q-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions
title_fullStr q-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions
title_full_unstemmed q-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions
title_sort q-hermite hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions
publisher Elsevier
series Journal of King Saud University: Science
issn 1018-3647
publishDate 2018-04-01
description In this paper, we prove the correct q-Hermite–Hadamard inequality, some new q-Hermite–Hadamard inequalities, and generalized q-Hermite–Hadamard inequality. By using the left hand part of the correct q-Hermite–Hadamard inequality, we have a new equality. Finally using the new equality, we give some q-midpoint type integral inequalities through q-differentiable convex and q-differentiable quasi-convex functions. Many results given in this paper provide extensions of others given in previous works. Keywords: Hermite–Hadamard inequality, Midpoint type inequality, q-Integral inequalities, q-Derivative, q-Integration, Convexity, Quasi-convexity
url http://www.sciencedirect.com/science/article/pii/S1018364716304839
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AT mehmetzekisarıkaya qhermitehadamardinequalitiesandquantumestimatesformidpointtypeinequalitiesviaconvexandquasiconvexfunctions
AT mehmetkunt qhermitehadamardinequalitiesandquantumestimatesformidpointtypeinequalitiesviaconvexandquasiconvexfunctions
AT imdatiscan qhermitehadamardinequalitiesandquantumestimatesformidpointtypeinequalitiesviaconvexandquasiconvexfunctions
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