Simpson- and Newton-Type Inequalities for Convex Functions via (<i>p</i>,<i>q</i>)-Calculus
In this paper, we establish several new <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></mr...
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| Format: | Article |
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MDPI AG
2021-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/12/1338 |
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| author | Waewta Luangboon Kamsing Nonlaopon Jessada Tariboon Sotiris K. Ntouyas |
| author_facet | Waewta Luangboon Kamsing Nonlaopon Jessada Tariboon Sotiris K. Ntouyas |
| author_sort | Waewta Luangboon |
| collection | DOAJ |
| description | In this paper, we establish several new <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>-integral identities involving <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 by using the definition of a <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>-derivative. These results are then used to derive <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>-integral Simpson- and Newton-type inequalities involving convex functions. Moreover, some examples are given to illustrate the investigated results. |
| first_indexed | 2024-03-10T10:33:17Z |
| format | Article |
| id | doaj.art-7b96a1ed415e4c1aa3662fcf86b43403 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T10:33:17Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-7b96a1ed415e4c1aa3662fcf86b434032023-11-21T23:28:20ZengMDPI AGMathematics2227-73902021-06-01912133810.3390/math9121338Simpson- and Newton-Type Inequalities for Convex Functions via (<i>p</i>,<i>q</i>)-CalculusWaewta Luangboon0Kamsing 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, 451 10 Ioannina, GreeceIn this paper, we establish several new <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>-integral identities involving <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 by using the definition of a <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>-derivative. These results are then used to derive <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>-integral Simpson- and Newton-type inequalities involving convex functions. Moreover, some examples are given to illustrate the investigated results.https://www.mdpi.com/2227-7390/9/12/1338Simpson inequalityNewton inequalityconvex function(<i>p</i>,<i>q</i>)-derivative(<i>p</i>,<i>q</i>)-integral(<i>p</i>,<i>q</i>)-calculus |
| spellingShingle | Waewta Luangboon Kamsing Nonlaopon Jessada Tariboon Sotiris K. Ntouyas Simpson- and Newton-Type Inequalities for Convex Functions via (<i>p</i>,<i>q</i>)-Calculus Mathematics Simpson inequality Newton inequality convex function (<i>p</i>,<i>q</i>)-derivative (<i>p</i>,<i>q</i>)-integral (<i>p</i>,<i>q</i>)-calculus |
| title | Simpson- and Newton-Type Inequalities for Convex Functions via (<i>p</i>,<i>q</i>)-Calculus |
| title_full | Simpson- and Newton-Type Inequalities for Convex Functions via (<i>p</i>,<i>q</i>)-Calculus |
| title_fullStr | Simpson- and Newton-Type Inequalities for Convex Functions via (<i>p</i>,<i>q</i>)-Calculus |
| title_full_unstemmed | Simpson- and Newton-Type Inequalities for Convex Functions via (<i>p</i>,<i>q</i>)-Calculus |
| title_short | Simpson- and Newton-Type Inequalities for Convex Functions via (<i>p</i>,<i>q</i>)-Calculus |
| title_sort | simpson and newton type inequalities for convex functions via i p i i q i calculus |
| topic | Simpson inequality Newton inequality convex function (<i>p</i>,<i>q</i>)-derivative (<i>p</i>,<i>q</i>)-integral (<i>p</i>,<i>q</i>)-calculus |
| url | https://www.mdpi.com/2227-7390/9/12/1338 |
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