Trapezoidal-Type Inequalities for Strongly Convex and Quasi-Convex Functions via Post-Quantum Calculus
In this paper, we establish new <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo><...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-09-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/10/1238 |
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| author | Humaira Kalsoom Miguel Vivas-Cortez Muhammad Amer Latif |
| author_facet | Humaira Kalsoom Miguel Vivas-Cortez Muhammad Amer Latif |
| author_sort | Humaira Kalsoom |
| collection | DOAJ |
| description | In this paper, we establish new <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow><msub><mrow></mrow><msub><mi>κ</mi><mn>1</mn></msub></msub></mrow></semantics></math></inline-formula>-integral and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow><msup><mrow></mrow><msub><mi>κ</mi><mn>2</mn></msub></msup></mrow></semantics></math></inline-formula>-integral identities. By employing these new identities, we establish new <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow><msub><mrow></mrow><msub><mi>κ</mi><mn>1</mn></msub></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow><msup><mrow></mrow><msub><mi>κ</mi><mn>2</mn></msub></msup></mrow></semantics></math></inline-formula>- trapezoidal integral-type inequalities through strongly convex and quasi-convex functions. Finally, some examples are given to illustrate the investigated results. |
| first_indexed | 2024-03-10T06:34:30Z |
| format | Article |
| id | doaj.art-423df7b7044041b49203537d6d70e90e |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T06:34:30Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-423df7b7044041b49203537d6d70e90e2023-11-22T18:09:54ZengMDPI AGEntropy1099-43002021-09-012310123810.3390/e23101238Trapezoidal-Type Inequalities for Strongly Convex and Quasi-Convex Functions via Post-Quantum CalculusHumaira Kalsoom0Miguel Vivas-Cortez1Muhammad Amer Latif2Department of Mathematical, Zhejiang Normal University, Jinhua 321004, ChinaEscuela de Ciencias Físicas y Matemáticas, Facultad de Ciencias Naturales y Exactas Pontificia Universidad Católica del Ecuador, Sede Quito 17-01-2184, EcuadorDepartment of Basic Sciences, Deanship of Preparatory Year, King Faisal University, Hofuf 31982, Al-Hasa, Saudi ArabiaIn this paper, we establish new <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow><msub><mrow></mrow><msub><mi>κ</mi><mn>1</mn></msub></msub></mrow></semantics></math></inline-formula>-integral and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow><msup><mrow></mrow><msub><mi>κ</mi><mn>2</mn></msub></msup></mrow></semantics></math></inline-formula>-integral identities. By employing these new identities, we establish new <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow><msub><mrow></mrow><msub><mi>κ</mi><mn>1</mn></msub></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow><msup><mrow></mrow><msub><mi>κ</mi><mn>2</mn></msub></msup></mrow></semantics></math></inline-formula>- trapezoidal integral-type inequalities through strongly convex and quasi-convex functions. Finally, some examples are given to illustrate the investigated results.https://www.mdpi.com/1099-4300/23/10/1238<i>(p,q)</i>-calculustrapezoidal <i>(p,q)</i><sub><i>κ</i>1</sub>-integral and <i>(p,q)</i><sup><i>κ</i>2</sup>-integralstrongly convex functionsstrongly quasi-convex functions |
| spellingShingle | Humaira Kalsoom Miguel Vivas-Cortez Muhammad Amer Latif Trapezoidal-Type Inequalities for Strongly Convex and Quasi-Convex Functions via Post-Quantum Calculus Entropy <i>(p,q)</i>-calculus trapezoidal <i>(p,q)</i><sub><i>κ</i>1</sub>-integral and <i>(p,q)</i><sup><i>κ</i>2</sup>-integral strongly convex functions strongly quasi-convex functions |
| title | Trapezoidal-Type Inequalities for Strongly Convex and Quasi-Convex Functions via Post-Quantum Calculus |
| title_full | Trapezoidal-Type Inequalities for Strongly Convex and Quasi-Convex Functions via Post-Quantum Calculus |
| title_fullStr | Trapezoidal-Type Inequalities for Strongly Convex and Quasi-Convex Functions via Post-Quantum Calculus |
| title_full_unstemmed | Trapezoidal-Type Inequalities for Strongly Convex and Quasi-Convex Functions via Post-Quantum Calculus |
| title_short | Trapezoidal-Type Inequalities for Strongly Convex and Quasi-Convex Functions via Post-Quantum Calculus |
| title_sort | trapezoidal type inequalities for strongly convex and quasi convex functions via post quantum calculus |
| topic | <i>(p,q)</i>-calculus trapezoidal <i>(p,q)</i><sub><i>κ</i>1</sub>-integral and <i>(p,q)</i><sup><i>κ</i>2</sup>-integral strongly convex functions strongly quasi-convex functions |
| url | https://www.mdpi.com/1099-4300/23/10/1238 |
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