Refinements of Hermite–Hadamard Inequalities for Continuous Convex Functions via (<i>p</i>,<i>q</i>)-Calculus
In this paper, we present some new refinements of Hermite–Hadamard inequalities for continuous convex functions by using <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p<...
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| Format: | Article |
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MDPI AG
2021-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/4/446 |
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| author | Julalak Prabseang Kamsing Nonlaopon Jessada Tariboon Sotiris K. Ntouyas |
| author_facet | Julalak Prabseang Kamsing Nonlaopon Jessada Tariboon Sotiris K. Ntouyas |
| author_sort | Julalak Prabseang |
| collection | DOAJ |
| description | In this paper, we present some new refinements of Hermite–Hadamard inequalities for continuous 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>-calculus. Moreover, we study some 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>-Hermite–Hadamard inequalities for multiple integrals. Many results given in this paper provide extensions of others given in previous research. |
| first_indexed | 2024-03-09T00:36:27Z |
| format | Article |
| id | doaj.art-60f016a5f5ee4dc6972a0042db4f16e5 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T00:36:27Z |
| publishDate | 2021-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-60f016a5f5ee4dc6972a0042db4f16e52023-12-11T18:06:42ZengMDPI AGMathematics2227-73902021-02-019444610.3390/math9040446Refinements of Hermite–Hadamard Inequalities for Continuous Convex Functions via (<i>p</i>,<i>q</i>)-CalculusJulalak Prabseang0Kamsing Nonlaopon1Jessada Tariboon2Sotiris K. Ntouyas3Department of Mathematics, Faculty of Science and Technology, Phetchaburi Rajabhat University, Phetchaburi 76000, 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 present some new refinements of Hermite–Hadamard inequalities for continuous 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>-calculus. Moreover, we study some 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>-Hermite–Hadamard inequalities for multiple integrals. Many results given in this paper provide extensions of others given in previous research.https://www.mdpi.com/2227-7390/9/4/446Hermite–Hadamard inequality(<i>p</i>,<i>q</i>)-derivative(<i>p</i>,<i>q</i>)-integralconvex functions |
| spellingShingle | Julalak Prabseang Kamsing Nonlaopon Jessada Tariboon Sotiris K. Ntouyas Refinements of Hermite–Hadamard Inequalities for Continuous 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 convex functions |
| title | Refinements of Hermite–Hadamard Inequalities for Continuous Convex Functions via (<i>p</i>,<i>q</i>)-Calculus |
| title_full | Refinements of Hermite–Hadamard Inequalities for Continuous Convex Functions via (<i>p</i>,<i>q</i>)-Calculus |
| title_fullStr | Refinements of Hermite–Hadamard Inequalities for Continuous Convex Functions via (<i>p</i>,<i>q</i>)-Calculus |
| title_full_unstemmed | Refinements of Hermite–Hadamard Inequalities for Continuous Convex Functions via (<i>p</i>,<i>q</i>)-Calculus |
| title_short | Refinements of Hermite–Hadamard Inequalities for Continuous Convex Functions via (<i>p</i>,<i>q</i>)-Calculus |
| title_sort | refinements of hermite hadamard inequalities for continuous 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 convex functions |
| url | https://www.mdpi.com/2227-7390/9/4/446 |
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