On Hermite-Hadamard Type Inequalities for Coordinated Convex Functions via (<i>p</i>,<i>q</i>)-Calculus

In this paper, we define <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></sema...

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Main Authors: Fongchan Wannalookkhee, Kamsing Nonlaopon, Jessada Tariboon, Sotiris K. Ntouyas
Format: Article
Language:English
Published: MDPI AG 2021-03-01
Series:Mathematics
Subjects:
Online Access:https://www.mdpi.com/2227-7390/9/7/698
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author Fongchan Wannalookkhee
Kamsing Nonlaopon
Jessada Tariboon
Sotiris K. Ntouyas
author_facet Fongchan Wannalookkhee
Kamsing Nonlaopon
Jessada Tariboon
Sotiris K. Ntouyas
author_sort Fongchan Wannalookkhee
collection DOAJ
description In this paper, we define <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-integrals for continuous functions of two variables. Then, we prove the Hermite-Hadamard type inequalities for coordinated convex functions by using <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-integrals. Many results obtained in this paper provide significant extensions of other related results given in the literature. Finally, we give some examples of our results.
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spelling doaj.art-0d205caca0754adbba27cf185d60fd662023-11-21T11:46:36ZengMDPI AGMathematics2227-73902021-03-019769810.3390/math9070698On Hermite-Hadamard Type Inequalities for Coordinated Convex Functions via (<i>p</i>,<i>q</i>)-CalculusFongchan Wannalookkhee0Kamsing Nonlaopon1Jessada Tariboon2Sotiris K. Ntouyas3Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandDepartment of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandDepartment of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, ThailandDepartment of Mathematics, University of Ioannina, 45110 Ioannina, GreeceIn this paper, we define <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-integrals for continuous functions of two variables. Then, we prove the Hermite-Hadamard type inequalities for coordinated convex functions by using <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-integrals. Many results obtained in this paper provide significant extensions of other related results given in the literature. Finally, we give some examples of our results.https://www.mdpi.com/2227-7390/9/7/698Hermite-Hadamard inequality(<i>p</i>,<i>q</i>)-derivative(<i>p</i>,<i>q</i>)-integral(<i>p</i>,<i>q</i>)-calculuscoordinated convex function
spellingShingle Fongchan Wannalookkhee
Kamsing Nonlaopon
Jessada Tariboon
Sotiris K. Ntouyas
On Hermite-Hadamard Type Inequalities for Coordinated Convex Functions via (<i>p</i>,<i>q</i>)-Calculus
Mathematics
Hermite-Hadamard inequality
(<i>p</i>,<i>q</i>)-derivative
(<i>p</i>,<i>q</i>)-integral
(<i>p</i>,<i>q</i>)-calculus
coordinated convex function
title On Hermite-Hadamard Type Inequalities for Coordinated Convex Functions via (<i>p</i>,<i>q</i>)-Calculus
title_full On Hermite-Hadamard Type Inequalities for Coordinated Convex Functions via (<i>p</i>,<i>q</i>)-Calculus
title_fullStr On Hermite-Hadamard Type Inequalities for Coordinated Convex Functions via (<i>p</i>,<i>q</i>)-Calculus
title_full_unstemmed On Hermite-Hadamard Type Inequalities for Coordinated Convex Functions via (<i>p</i>,<i>q</i>)-Calculus
title_short On Hermite-Hadamard Type Inequalities for Coordinated Convex Functions via (<i>p</i>,<i>q</i>)-Calculus
title_sort on hermite hadamard type inequalities for coordinated convex functions via i p i i q i calculus
topic Hermite-Hadamard inequality
(<i>p</i>,<i>q</i>)-derivative
(<i>p</i>,<i>q</i>)-integral
(<i>p</i>,<i>q</i>)-calculus
coordinated convex function
url https://www.mdpi.com/2227-7390/9/7/698
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