A Generalization of Hermite–Hadamard–Fejer Type Inequalities for the p-Convex Function via α-Generator
In the 17th century, I. Newton and G. Leibniz found independently each other the basic operations of calculus, i.e., differentiation and integration. And this development broke new ground in mathematics. From 1967 to 1970, Michael Grossman and Robert Katz gave definitions of a new kind of derivative...
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/1185960 |
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| author | Erdal Ünlüyol Yeter Erdaş |
| author_facet | Erdal Ünlüyol Yeter Erdaş |
| author_sort | Erdal Ünlüyol |
| collection | DOAJ |
| description | In the 17th century, I. Newton and G. Leibniz found independently each other the basic operations of calculus, i.e., differentiation and integration. And this development broke new ground in mathematics. From 1967 to 1970, Michael Grossman and Robert Katz gave definitions of a new kind of derivative and integral, converting the roles of subtraction and addition into division and multiplication, respectively. And then they generalised this operation. Later, they named this analysis non-Newtonian calculus. This calculus is basically generated by generators. So, in this article, first, we give the definition of the p-convex function due to α-generator. Second, we obtain some new theorems for this function with respect to the α-generator. Third, we get some new theorems using Hermite–Hadamard–Fejer inequality for the αp-convex function. Finally, we show that our obtained results are reduced to the classical case in the special conditions. |
| format | Article |
| id | doaj-art-7a264a176baf43c7a7658da28d6b4cac |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-7a264a176baf43c7a7658da28d6b4cac2025-02-03T06:47:16ZengWileyJournal of Mathematics2314-47852023-01-01202310.1155/2023/1185960A Generalization of Hermite–Hadamard–Fejer Type Inequalities for the p-Convex Function via α-GeneratorErdal Ünlüyol0Yeter Erdaş1Ordu UniversityOrdu UniversityIn the 17th century, I. Newton and G. Leibniz found independently each other the basic operations of calculus, i.e., differentiation and integration. And this development broke new ground in mathematics. From 1967 to 1970, Michael Grossman and Robert Katz gave definitions of a new kind of derivative and integral, converting the roles of subtraction and addition into division and multiplication, respectively. And then they generalised this operation. Later, they named this analysis non-Newtonian calculus. This calculus is basically generated by generators. So, in this article, first, we give the definition of the p-convex function due to α-generator. Second, we obtain some new theorems for this function with respect to the α-generator. Third, we get some new theorems using Hermite–Hadamard–Fejer inequality for the αp-convex function. Finally, we show that our obtained results are reduced to the classical case in the special conditions.http://dx.doi.org/10.1155/2023/1185960 |
| spellingShingle | Erdal Ünlüyol Yeter Erdaş A Generalization of Hermite–Hadamard–Fejer Type Inequalities for the p-Convex Function via α-Generator Journal of Mathematics |
| title | A Generalization of Hermite–Hadamard–Fejer Type Inequalities for the p-Convex Function via α-Generator |
| title_full | A Generalization of Hermite–Hadamard–Fejer Type Inequalities for the p-Convex Function via α-Generator |
| title_fullStr | A Generalization of Hermite–Hadamard–Fejer Type Inequalities for the p-Convex Function via α-Generator |
| title_full_unstemmed | A Generalization of Hermite–Hadamard–Fejer Type Inequalities for the p-Convex Function via α-Generator |
| title_short | A Generalization of Hermite–Hadamard–Fejer Type Inequalities for the p-Convex Function via α-Generator |
| title_sort | generalization of hermite hadamard fejer type inequalities for the p convex function via α generator |
| url | http://dx.doi.org/10.1155/2023/1185960 |
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