Regularity properties and integral inequalities related to (k; h1; h2)-convexity of functions
The class of (k; h1; h2)-convex functions is introduced, together with some particular classes of corresponding generalized convex dominated functions. Few regularity properties of (k; h1; h2)-convex functions are proved by means of Bernstein-Doetsch type results. Also we find conditions in which ev...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Sciendo
2015-07-01
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| Series: | Annals of the West University of Timisoara: Mathematics and Computer Science |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/awutm-2015-0002 |
| _version_ | 1828262688317243392 |
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| author | Cristescu Gabriela Găianu Mihail Muhammad Uzair Awan |
| author_facet | Cristescu Gabriela Găianu Mihail Muhammad Uzair Awan |
| author_sort | Cristescu Gabriela |
| collection | DOAJ |
| description | The class of (k; h1; h2)-convex functions is introduced, together with some particular classes of corresponding generalized convex dominated functions. Few regularity properties of (k; h1; h2)-convex functions are proved by means of Bernstein-Doetsch type results. Also we find conditions in which every local minimizer of a (k; h1; h2)-convex function is global. Classes of (k; h1; h2)-convex functions, which allow integral upper bounds of Hermite-Hadamard type, are identified. Hermite-Hadamard type inequalities are also obtained in a particular class of the (k; h1; h2)- convex dominated functions. |
| first_indexed | 2024-04-13T03:59:39Z |
| format | Article |
| id | doaj.art-2a1ccd80fe7842fab7b92f9ec40be0fd |
| institution | Directory Open Access Journal |
| issn | 1841-3307 |
| language | English |
| last_indexed | 2024-04-13T03:59:39Z |
| publishDate | 2015-07-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Annals of the West University of Timisoara: Mathematics and Computer Science |
| spelling | doaj.art-2a1ccd80fe7842fab7b92f9ec40be0fd2022-12-22T03:03:31ZengSciendoAnnals of the West University of Timisoara: Mathematics and Computer Science1841-33072015-07-01531193510.1515/awutm-2015-0002awutm-2015-0002Regularity properties and integral inequalities related to (k; h1; h2)-convexity of functionsCristescu Gabriela0Găianu Mihail1Muhammad Uzair Awan2Department of Mathematics and Computer Sciences Aurel Vlaicu University of Arad Bd. Revoluției nr.77, Arad, RomâniaDepartment of Computer Sciences West University of Timișoara, Vasile Pârvan nr. 4, Timișoara, RomâniaDepartment of Mathematics, COMSATS Institute of Information Technology, Park Road, Islamabad, PakistanThe class of (k; h1; h2)-convex functions is introduced, together with some particular classes of corresponding generalized convex dominated functions. Few regularity properties of (k; h1; h2)-convex functions are proved by means of Bernstein-Doetsch type results. Also we find conditions in which every local minimizer of a (k; h1; h2)-convex function is global. Classes of (k; h1; h2)-convex functions, which allow integral upper bounds of Hermite-Hadamard type, are identified. Hermite-Hadamard type inequalities are also obtained in a particular class of the (k; h1; h2)- convex dominated functions.https://doi.org/10.1515/awutm-2015-0002generalized convex functionconvex-dominated functionbernstein-doetsch theoremhermite- hadamard’s inequalityregularity properties |
| spellingShingle | Cristescu Gabriela Găianu Mihail Muhammad Uzair Awan Regularity properties and integral inequalities related to (k; h1; h2)-convexity of functions Annals of the West University of Timisoara: Mathematics and Computer Science generalized convex function convex-dominated function bernstein-doetsch theorem hermite- hadamard’s inequality regularity properties |
| title | Regularity properties and integral inequalities related to (k; h1; h2)-convexity of functions |
| title_full | Regularity properties and integral inequalities related to (k; h1; h2)-convexity of functions |
| title_fullStr | Regularity properties and integral inequalities related to (k; h1; h2)-convexity of functions |
| title_full_unstemmed | Regularity properties and integral inequalities related to (k; h1; h2)-convexity of functions |
| title_short | Regularity properties and integral inequalities related to (k; h1; h2)-convexity of functions |
| title_sort | regularity properties and integral inequalities related to k h1 h2 convexity of functions |
| topic | generalized convex function convex-dominated function bernstein-doetsch theorem hermite- hadamard’s inequality regularity properties |
| url | https://doi.org/10.1515/awutm-2015-0002 |
| work_keys_str_mv | AT cristescugabriela regularitypropertiesandintegralinequalitiesrelatedtokh1h2convexityoffunctions AT gaianumihail regularitypropertiesandintegralinequalitiesrelatedtokh1h2convexityoffunctions AT muhammaduzairawan regularitypropertiesandintegralinequalitiesrelatedtokh1h2convexityoffunctions |