On Some Generalized Simpson’s and Newton’s Inequalities for (<i>α</i>, <i>m</i>)-Convex Functions in <i>q</i>-Calculus
In this paper, we first establish two right-quantum integral equalities involving a right-quantum derivative and a parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mo>...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/24/3266 |
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| author | Ifra Bashir Sial Sun Mei Muhammad Aamir Ali Kamsing Nonlaopon |
| author_facet | Ifra Bashir Sial Sun Mei Muhammad Aamir Ali Kamsing Nonlaopon |
| author_sort | Ifra Bashir Sial |
| collection | DOAJ |
| description | In this paper, we first establish two right-quantum integral equalities involving a right-quantum derivative and a parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mo>∈</mo><mo> </mo><mfenced separators="" open="[" close="]"><mn>0</mn><mo>,</mo><mn>1</mn></mfenced></mrow></semantics></math></inline-formula>. Then, we prove modified versions of Simpson’s and Newton’s type inequalities using established equalities for right-quantum differentiable <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfenced separators="" open="(" close=")"><mi>α</mi><mo>,</mo><mi>m</mi></mfenced></semantics></math></inline-formula>-convex functions. The newly developed inequalities are also proven to be expansions of comparable inequalities found in the literature. |
| first_indexed | 2024-03-10T03:36:54Z |
| format | Article |
| id | doaj.art-2889e53684564e90bc34743f781a9c6a |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:36:54Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-2889e53684564e90bc34743f781a9c6a2023-11-23T09:26:39ZengMDPI AGMathematics2227-73902021-12-01924326610.3390/math9243266On Some Generalized Simpson’s and Newton’s Inequalities for (<i>α</i>, <i>m</i>)-Convex Functions in <i>q</i>-CalculusIfra Bashir Sial0Sun Mei1Muhammad Aamir Ali2Kamsing Nonlaopon3School of Mathematics Science, Jiangsu University, Zhenjiang 212114, ChinaSchool of Mathematics Science, Jiangsu University, Zhenjiang 212114, ChinaJiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, ChinaDepartment of Mathematics, Faculty of Science and Arts, Khon Kaen University, Khon Kaen 40002, ThailandIn this paper, we first establish two right-quantum integral equalities involving a right-quantum derivative and a parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mo>∈</mo><mo> </mo><mfenced separators="" open="[" close="]"><mn>0</mn><mo>,</mo><mn>1</mn></mfenced></mrow></semantics></math></inline-formula>. Then, we prove modified versions of Simpson’s and Newton’s type inequalities using established equalities for right-quantum differentiable <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfenced separators="" open="(" close=")"><mi>α</mi><mo>,</mo><mi>m</mi></mfenced></semantics></math></inline-formula>-convex functions. The newly developed inequalities are also proven to be expansions of comparable inequalities found in the literature.https://www.mdpi.com/2227-7390/9/24/3266Simpson’s inequalitiesNewton’s inequalitiesquantum calculus(<i>α</i>, <i>m</i>)-convex functions |
| spellingShingle | Ifra Bashir Sial Sun Mei Muhammad Aamir Ali Kamsing Nonlaopon On Some Generalized Simpson’s and Newton’s Inequalities for (<i>α</i>, <i>m</i>)-Convex Functions in <i>q</i>-Calculus Mathematics Simpson’s inequalities Newton’s inequalities quantum calculus (<i>α</i>, <i>m</i>)-convex functions |
| title | On Some Generalized Simpson’s and Newton’s Inequalities for (<i>α</i>, <i>m</i>)-Convex Functions in <i>q</i>-Calculus |
| title_full | On Some Generalized Simpson’s and Newton’s Inequalities for (<i>α</i>, <i>m</i>)-Convex Functions in <i>q</i>-Calculus |
| title_fullStr | On Some Generalized Simpson’s and Newton’s Inequalities for (<i>α</i>, <i>m</i>)-Convex Functions in <i>q</i>-Calculus |
| title_full_unstemmed | On Some Generalized Simpson’s and Newton’s Inequalities for (<i>α</i>, <i>m</i>)-Convex Functions in <i>q</i>-Calculus |
| title_short | On Some Generalized Simpson’s and Newton’s Inequalities for (<i>α</i>, <i>m</i>)-Convex Functions in <i>q</i>-Calculus |
| title_sort | on some generalized simpson s and newton s inequalities for i α i i m i convex functions in i q i calculus |
| topic | Simpson’s inequalities Newton’s inequalities quantum calculus (<i>α</i>, <i>m</i>)-convex functions |
| url | https://www.mdpi.com/2227-7390/9/24/3266 |
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