Post-Quantum Chebyshev-Type Integral Inequalities for Synchronous Functions
In this paper, we apply <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></seman...
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MDPI AG
2022-01-01
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| Online Access: | https://www.mdpi.com/2227-7390/10/3/468 |
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| author | Nuttapong Arunrat Keaitsuda Maneeruk Nakprasit Kamsing Nonlaopon Praveen Agarwal Sotiris K. Ntouyas |
| author_facet | Nuttapong Arunrat Keaitsuda Maneeruk Nakprasit Kamsing Nonlaopon Praveen Agarwal Sotiris K. Ntouyas |
| author_sort | Nuttapong Arunrat |
| collection | DOAJ |
| description | In this paper, we apply <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 to establish some new Chebyshev-type integral inequalities for synchronous functions. In particular, we generalize results of quantum Chebyshev-type integral inequalities 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>-integral. By taking <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>q</mi><mo>→</mo><mn>1</mn></mrow></semantics></math></inline-formula>, our results reduce to classical results on Chebyshev-type inequalities for synchronous functions. Furthermore, we consider their relevance with other related known results. |
| first_indexed | 2024-03-09T23:31:44Z |
| format | Article |
| id | doaj.art-f74502487bd2415ca73b82f3bd9b9290 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:31:44Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-f74502487bd2415ca73b82f3bd9b92902023-11-23T17:08:00ZengMDPI AGMathematics2227-73902022-01-0110346810.3390/math10030468Post-Quantum Chebyshev-Type Integral Inequalities for Synchronous FunctionsNuttapong Arunrat0Keaitsuda Maneeruk Nakprasit1Kamsing Nonlaopon2Praveen Agarwal3Sotiris K. Ntouyas4Department 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 Science, Khon Kaen University, Khon Kaen 40002, ThailandDepartment of Mathematics, Anand International College of Engineering, Jaipur 302029, IndiaDepartment of Mathematics, University of Ioannina, 45110 Ioannina, GreeceIn this paper, we apply <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 to establish some new Chebyshev-type integral inequalities for synchronous functions. In particular, we generalize results of quantum Chebyshev-type integral inequalities 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>-integral. By taking <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>q</mi><mo>→</mo><mn>1</mn></mrow></semantics></math></inline-formula>, our results reduce to classical results on Chebyshev-type inequalities for synchronous functions. Furthermore, we consider their relevance with other related known results.https://www.mdpi.com/2227-7390/10/3/468Chebyshev-type inequalitiessynchronous (asynchronous) functions(<i>p</i>,<i>q</i>)-calculus(<i>p</i>,<i>q</i>)-derivative(<i>p</i>,<i>q</i>)-integral |
| spellingShingle | Nuttapong Arunrat Keaitsuda Maneeruk Nakprasit Kamsing Nonlaopon Praveen Agarwal Sotiris K. Ntouyas Post-Quantum Chebyshev-Type Integral Inequalities for Synchronous Functions Mathematics Chebyshev-type inequalities synchronous (asynchronous) functions (<i>p</i>,<i>q</i>)-calculus (<i>p</i>,<i>q</i>)-derivative (<i>p</i>,<i>q</i>)-integral |
| title | Post-Quantum Chebyshev-Type Integral Inequalities for Synchronous Functions |
| title_full | Post-Quantum Chebyshev-Type Integral Inequalities for Synchronous Functions |
| title_fullStr | Post-Quantum Chebyshev-Type Integral Inequalities for Synchronous Functions |
| title_full_unstemmed | Post-Quantum Chebyshev-Type Integral Inequalities for Synchronous Functions |
| title_short | Post-Quantum Chebyshev-Type Integral Inequalities for Synchronous Functions |
| title_sort | post quantum chebyshev type integral inequalities for synchronous functions |
| topic | Chebyshev-type inequalities synchronous (asynchronous) functions (<i>p</i>,<i>q</i>)-calculus (<i>p</i>,<i>q</i>)-derivative (<i>p</i>,<i>q</i>)-integral |
| url | https://www.mdpi.com/2227-7390/10/3/468 |
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