Hermite–Hadamard-Type Inequalities and Two-Point Quadrature Formula
As convexity plays an important role in many aspects of mathematical programming, e.g., for obtaining sufficient optimality conditions and in duality theorems, and one of the most important inequalities for convex functions is the Hermite–Hadamard inequality, the importance of this paper lies in pro...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/9/1432 |
| _version_ | 1797503898519339008 |
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| author | Josipa Barić |
| author_facet | Josipa Barić |
| author_sort | Josipa Barić |
| collection | DOAJ |
| description | As convexity plays an important role in many aspects of mathematical programming, e.g., for obtaining sufficient optimality conditions and in duality theorems, and one of the most important inequalities for convex functions is the Hermite–Hadamard inequality, the importance of this paper lies in providing some new improvements for convex functions and new directions in studying new variants of the Hermite–Hadamard inequality. The first part of the article includes some known concepts regarding convex functions and related inequalities. In the second part of the study, a derivation of the Hermite–Hadamard inequality for convex functions of higher order is given, emphasizing the purpose and importance of some quadrature formulas. In the third section, the applications of the main results are presented by obtaining Hermite–Hadamard-type estimates for various classical quadrature formulas such as the Gauss–Legendre two-point quadrature formula and the Gauss–Chebyshev two-point quadrature formulas of the first and second kind. |
| first_indexed | 2024-03-10T03:56:57Z |
| format | Article |
| id | doaj.art-cd4a760c37114202bf343418c2791235 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:56:57Z |
| publishDate | 2022-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-cd4a760c37114202bf343418c27912352023-11-23T08:44:14ZengMDPI AGMathematics2227-73902022-04-01109143210.3390/math10091432Hermite–Hadamard-Type Inequalities and Two-Point Quadrature FormulaJosipa Barić0Faculty of Electrical Engineering Mechanical Engineering and Naval Architecture, University of Split, Rudjera Boškovića 32, 21 000 Split, CroatiaAs convexity plays an important role in many aspects of mathematical programming, e.g., for obtaining sufficient optimality conditions and in duality theorems, and one of the most important inequalities for convex functions is the Hermite–Hadamard inequality, the importance of this paper lies in providing some new improvements for convex functions and new directions in studying new variants of the Hermite–Hadamard inequality. The first part of the article includes some known concepts regarding convex functions and related inequalities. In the second part of the study, a derivation of the Hermite–Hadamard inequality for convex functions of higher order is given, emphasizing the purpose and importance of some quadrature formulas. In the third section, the applications of the main results are presented by obtaining Hermite–Hadamard-type estimates for various classical quadrature formulas such as the Gauss–Legendre two-point quadrature formula and the Gauss–Chebyshev two-point quadrature formulas of the first and second kind.https://www.mdpi.com/2227-7390/10/9/1432Hermite–Hadamard inequalitiesweighted two-point formulahigher-order convex functionsw-harmonic sequences of functions |
| spellingShingle | Josipa Barić Hermite–Hadamard-Type Inequalities and Two-Point Quadrature Formula Mathematics Hermite–Hadamard inequalities weighted two-point formula higher-order convex functions w-harmonic sequences of functions |
| title | Hermite–Hadamard-Type Inequalities and Two-Point Quadrature Formula |
| title_full | Hermite–Hadamard-Type Inequalities and Two-Point Quadrature Formula |
| title_fullStr | Hermite–Hadamard-Type Inequalities and Two-Point Quadrature Formula |
| title_full_unstemmed | Hermite–Hadamard-Type Inequalities and Two-Point Quadrature Formula |
| title_short | Hermite–Hadamard-Type Inequalities and Two-Point Quadrature Formula |
| title_sort | hermite hadamard type inequalities and two point quadrature formula |
| topic | Hermite–Hadamard inequalities weighted two-point formula higher-order convex functions w-harmonic sequences of functions |
| url | https://www.mdpi.com/2227-7390/10/9/1432 |
| work_keys_str_mv | AT josipabaric hermitehadamardtypeinequalitiesandtwopointquadratureformula |