Some Interesting Inequalities for the Class of Generalized Convex Functions of Higher Order
In this paper, we study a generalized version of strongly reciprocally convex functions of higher order. Firstly, we prove some basic properties for addition, scalar multiplication, and composition of functions. Secondly, we establish Hermite-Hadamard and Fejér type inequalities for the generalized...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2023-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2023/4759187 |
| _version_ | 1797733128354136064 |
|---|---|
| author | Limei Liu Muhammad Shoaib Saleem Faisal Yasin Kiran Naseem Aslam Pengfei Wang |
| author_facet | Limei Liu Muhammad Shoaib Saleem Faisal Yasin Kiran Naseem Aslam Pengfei Wang |
| author_sort | Limei Liu |
| collection | DOAJ |
| description | In this paper, we study a generalized version of strongly reciprocally convex functions of higher order. Firstly, we prove some basic properties for addition, scalar multiplication, and composition of functions. Secondly, we establish Hermite-Hadamard and Fejér type inequalities for the generalized version of strongly reciprocally convex functions of higher order. We also include some fractional integral inequalities concerning with this class of functions. Our results have applications in optimization theory and can be considered extension/generalization of many existing results. |
| first_indexed | 2024-03-12T12:24:39Z |
| format | Article |
| id | doaj.art-650b70f692284383ad09dfa531578c3e |
| institution | Directory Open Access Journal |
| issn | 2314-8888 |
| language | English |
| last_indexed | 2024-03-12T12:24:39Z |
| publishDate | 2023-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj.art-650b70f692284383ad09dfa531578c3e2023-08-30T00:00:02ZengHindawi LimitedJournal of Function Spaces2314-88882023-01-01202310.1155/2023/4759187Some Interesting Inequalities for the Class of Generalized Convex Functions of Higher OrderLimei Liu0Muhammad Shoaib Saleem1Faisal Yasin2Kiran Naseem Aslam3Pengfei Wang4General Studies Teaching DepartmentDepartment of MathematicsDepartment of Mathematics and StatisticsDepartment of MathematicsDepartment of MathematicsIn this paper, we study a generalized version of strongly reciprocally convex functions of higher order. Firstly, we prove some basic properties for addition, scalar multiplication, and composition of functions. Secondly, we establish Hermite-Hadamard and Fejér type inequalities for the generalized version of strongly reciprocally convex functions of higher order. We also include some fractional integral inequalities concerning with this class of functions. Our results have applications in optimization theory and can be considered extension/generalization of many existing results.http://dx.doi.org/10.1155/2023/4759187 |
| spellingShingle | Limei Liu Muhammad Shoaib Saleem Faisal Yasin Kiran Naseem Aslam Pengfei Wang Some Interesting Inequalities for the Class of Generalized Convex Functions of Higher Order Journal of Function Spaces |
| title | Some Interesting Inequalities for the Class of Generalized Convex Functions of Higher Order |
| title_full | Some Interesting Inequalities for the Class of Generalized Convex Functions of Higher Order |
| title_fullStr | Some Interesting Inequalities for the Class of Generalized Convex Functions of Higher Order |
| title_full_unstemmed | Some Interesting Inequalities for the Class of Generalized Convex Functions of Higher Order |
| title_short | Some Interesting Inequalities for the Class of Generalized Convex Functions of Higher Order |
| title_sort | some interesting inequalities for the class of generalized convex functions of higher order |
| url | http://dx.doi.org/10.1155/2023/4759187 |
| work_keys_str_mv | AT limeiliu someinterestinginequalitiesfortheclassofgeneralizedconvexfunctionsofhigherorder AT muhammadshoaibsaleem someinterestinginequalitiesfortheclassofgeneralizedconvexfunctionsofhigherorder AT faisalyasin someinterestinginequalitiesfortheclassofgeneralizedconvexfunctionsofhigherorder AT kirannaseemaslam someinterestinginequalitiesfortheclassofgeneralizedconvexfunctionsofhigherorder AT pengfeiwang someinterestinginequalitiesfortheclassofgeneralizedconvexfunctionsofhigherorder |