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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2021-03-01
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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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institution | Directory Open Access Journal |
issn | 2227-7390 |
language | English |
last_indexed | 2024-03-10T12:57:43Z |
publishDate | 2021-03-01 |
publisher | MDPI AG |
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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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