A note on h-convex functions
In this work, we discuss the continuity of $h$-convex functions by introducing the concepts of $h$-convex curves ($h$-cord). Geometric interpretation of $h$-convexity is given. The fact that for a $h$-continuous function $f$, is being $h$-convex if and only if is $h$-midconvex is proved. Generally,...
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| Format: | Article |
| Language: | English |
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EJAAM
2019-12-01
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| Series: | E-Journal of Analysis and Applied Mathematics |
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| Online Access: | https://ejaam.org/articles/2019/10.2478-ejaam-2019-0004.pdf |
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| author | Mohammad W. Alomari |
| author_facet | Mohammad W. Alomari |
| author_sort | Mohammad W. Alomari |
| collection | DOAJ |
| description | In this work, we discuss the continuity of $h$-convex functions by introducing the concepts of $h$-convex curves ($h$-cord). Geometric interpretation of $h$-convexity is given. The fact that for a $h$-continuous function $f$, is being $h$-convex if and only if is $h$-midconvex is proved. Generally, we prove that if $f$ is $h$-convex then $f$ is $h$-continuous. A discussion regarding derivative characterization of $h$-convexity is also proposed. |
| format | Article |
| id | doaj-art-c53c2bcf9faf47e2bcb92cd30c3b6d26 |
| institution | Kabale University |
| issn | 2544-9990 |
| language | English |
| publishDate | 2019-12-01 |
| publisher | EJAAM |
| record_format | Article |
| series | E-Journal of Analysis and Applied Mathematics |
| spelling | doaj-art-c53c2bcf9faf47e2bcb92cd30c3b6d262025-02-08T18:35:22ZengEJAAME-Journal of Analysis and Applied Mathematics2544-99902019-12-01201910.2478/ejaam-2019-0004A note on h-convex functionsMohammad W. Alomari0Department of Mathematics, Faculty of Science and Information Technology, Irbid National University, 2600 Irbid 21110, JordanIn this work, we discuss the continuity of $h$-convex functions by introducing the concepts of $h$-convex curves ($h$-cord). Geometric interpretation of $h$-convexity is given. The fact that for a $h$-continuous function $f$, is being $h$-convex if and only if is $h$-midconvex is proved. Generally, we prove that if $f$ is $h$-convex then $f$ is $h$-continuous. A discussion regarding derivative characterization of $h$-convexity is also proposed.https://ejaam.org/articles/2019/10.2478-ejaam-2019-0004.pdfh-convex functionhölder continuous |
| spellingShingle | Mohammad W. Alomari A note on h-convex functions E-Journal of Analysis and Applied Mathematics h-convex function hölder continuous |
| title | A note on h-convex functions |
| title_full | A note on h-convex functions |
| title_fullStr | A note on h-convex functions |
| title_full_unstemmed | A note on h-convex functions |
| title_short | A note on h-convex functions |
| title_sort | note on h convex functions |
| topic | h-convex function hölder continuous |
| url | https://ejaam.org/articles/2019/10.2478-ejaam-2019-0004.pdf |
| work_keys_str_mv | AT mohammadwalomari anoteonhconvexfunctions AT mohammadwalomari noteonhconvexfunctions |