Simpson’s Second-Type Inequalities for Co-Ordinated Convex Functions and Applications for Cubature Formulas
Inequality theory has attracted considerable attention from scientists because it can be used in many fields. In particular, Hermite–Hadamard and Simpson inequalities based on convex functions have become a cornerstone in pure and applied mathematics. We deal with Simpson’s second-type inequalities...
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MDPI AG
2022-01-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/1/33 |
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| author | Sabah Iftikhar Samet Erden Muhammad Aamir Ali Jamel Baili Hijaz Ahmad |
| author_facet | Sabah Iftikhar Samet Erden Muhammad Aamir Ali Jamel Baili Hijaz Ahmad |
| author_sort | Sabah Iftikhar |
| collection | DOAJ |
| description | Inequality theory has attracted considerable attention from scientists because it can be used in many fields. In particular, Hermite–Hadamard and Simpson inequalities based on convex functions have become a cornerstone in pure and applied mathematics. We deal with Simpson’s second-type inequalities based on coordinated convex functions in this work. In this paper, we first introduce Simpson’s second-type integral inequalities for two-variable functions whose second-order partial derivatives in modulus are convex on the coordinates. In addition, similar results are acquired by considering that powers of the absolute value of second-order partial derivatives of these two-variable functions are convex on the coordinates. Finally, some applications for Simpson’s <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><mo>/</mo><mn>8</mn></mrow></semantics></math></inline-formula> cubature formula are given. |
| first_indexed | 2024-03-10T01:26:55Z |
| format | Article |
| id | doaj.art-8f250a9b08ff4d74bda849b9a74bc008 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T01:26:55Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-8f250a9b08ff4d74bda849b9a74bc0082023-11-23T13:48:59ZengMDPI AGFractal and Fractional2504-31102022-01-01613310.3390/fractalfract6010033Simpson’s Second-Type Inequalities for Co-Ordinated Convex Functions and Applications for Cubature FormulasSabah Iftikhar0Samet Erden1Muhammad Aamir Ali2Jamel Baili3Hijaz Ahmad4Department of Mathematics, Xiamen University Malaysia, Sepang 43900, MalaysiaDepartment of Mathematics, Faculty of Science, Bartın University, Bartin 74100, TurkeyJiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, ChinaDepartment of Computer Engineering, College of Computer Science, King Khalid University, Abha 61413, Saudi ArabiaSection of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, ItalyInequality theory has attracted considerable attention from scientists because it can be used in many fields. In particular, Hermite–Hadamard and Simpson inequalities based on convex functions have become a cornerstone in pure and applied mathematics. We deal with Simpson’s second-type inequalities based on coordinated convex functions in this work. In this paper, we first introduce Simpson’s second-type integral inequalities for two-variable functions whose second-order partial derivatives in modulus are convex on the coordinates. In addition, similar results are acquired by considering that powers of the absolute value of second-order partial derivatives of these two-variable functions are convex on the coordinates. Finally, some applications for Simpson’s <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><mo>/</mo><mn>8</mn></mrow></semantics></math></inline-formula> cubature formula are given.https://www.mdpi.com/2504-3110/6/1/33coordinated convex functionsSimpson’s type inequality |
| spellingShingle | Sabah Iftikhar Samet Erden Muhammad Aamir Ali Jamel Baili Hijaz Ahmad Simpson’s Second-Type Inequalities for Co-Ordinated Convex Functions and Applications for Cubature Formulas Fractal and Fractional coordinated convex functions Simpson’s type inequality |
| title | Simpson’s Second-Type Inequalities for Co-Ordinated Convex Functions and Applications for Cubature Formulas |
| title_full | Simpson’s Second-Type Inequalities for Co-Ordinated Convex Functions and Applications for Cubature Formulas |
| title_fullStr | Simpson’s Second-Type Inequalities for Co-Ordinated Convex Functions and Applications for Cubature Formulas |
| title_full_unstemmed | Simpson’s Second-Type Inequalities for Co-Ordinated Convex Functions and Applications for Cubature Formulas |
| title_short | Simpson’s Second-Type Inequalities for Co-Ordinated Convex Functions and Applications for Cubature Formulas |
| title_sort | simpson s second type inequalities for co ordinated convex functions and applications for cubature formulas |
| topic | coordinated convex functions Simpson’s type inequality |
| url | https://www.mdpi.com/2504-3110/6/1/33 |
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