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Article: Hermite–Hadamard inequality for semiconvex functions of rate (k1,k2) on the coordinates and optimal mass transportation
| Title | Hermite–Hadamard inequality for semiconvex functions of rate (k1,k2) on the coordinates and optimal mass transportation |
|---|---|
| Authors | |
| Keywords | Convex functions Hermite-Hadamard integral inequality Optimal mass transportation |
| Issue Date | 2020 |
| Publisher | Rocky Mountain Mathematics Consortium. The Journal's web site is located at https://rmmc.eas.asu.edu/rmj/rmj.html |
| Citation | Rocky Mountain Journal of Mathematics, 2020, v. 50 n. 6, p. 2011-2021 How to Cite? |
| Abstract | We give a new Hermite-Hadamard inequality for a function f V [a; b]×[c; d] ⊂ R2→R which is semiconvex of rate .k1; k2/ on the coordinates. This generalizes some existing results on Hermite-Hadamard inequalities of S. S. Dragomir. In addition, we explain the Hermite-Hadamard inequality from the point of view of optimal mass transportation with cost function c(x; y) VD f (y-x)+ k1 2 jx1-y1j2+ k2 2 jx2-y2j2, where f ( ) : [a; b]×[c; d]→[0;∞] is semiconvex of rate .k1; k2/ on the coordinates and x = (x1; x2), y D .y1; y2/ 2 [a; b] × [c; d]. © 2020 Rocky Mountain Mathematics Consortium. All rights reserved. |
| Persistent Identifier | http://hdl.handle.net/10722/299314 |
| ISSN | 2023 Impact Factor: 0.7 2023 SCImago Journal Rankings: 0.424 |
| ISI Accession Number ID |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Chen, P | - |
| dc.contributor.author | Cheung, WS | - |
| dc.date.accessioned | 2021-05-10T07:00:02Z | - |
| dc.date.available | 2021-05-10T07:00:02Z | - |
| dc.date.issued | 2020 | - |
| dc.identifier.citation | Rocky Mountain Journal of Mathematics, 2020, v. 50 n. 6, p. 2011-2021 | - |
| dc.identifier.issn | 0035-7596 | - |
| dc.identifier.uri | http://hdl.handle.net/10722/299314 | - |
| dc.description.abstract | We give a new Hermite-Hadamard inequality for a function f V [a; b]×[c; d] ⊂ R2→R which is semiconvex of rate .k1; k2/ on the coordinates. This generalizes some existing results on Hermite-Hadamard inequalities of S. S. Dragomir. In addition, we explain the Hermite-Hadamard inequality from the point of view of optimal mass transportation with cost function c(x; y) VD f (y-x)+ k1 2 jx1-y1j2+ k2 2 jx2-y2j2, where f ( ) : [a; b]×[c; d]→[0;∞] is semiconvex of rate .k1; k2/ on the coordinates and x = (x1; x2), y D .y1; y2/ 2 [a; b] × [c; d]. © 2020 Rocky Mountain Mathematics Consortium. All rights reserved. | - |
| dc.language | eng | - |
| dc.publisher | Rocky Mountain Mathematics Consortium. The Journal's web site is located at https://rmmc.eas.asu.edu/rmj/rmj.html | - |
| dc.relation.ispartof | Rocky Mountain Journal of Mathematics | - |
| dc.subject | Convex functions | - |
| dc.subject | Hermite-Hadamard integral inequality | - |
| dc.subject | Optimal mass transportation | - |
| dc.title | Hermite–Hadamard inequality for semiconvex functions of rate (k1,k2) on the coordinates and optimal mass transportation | - |
| dc.type | Article | - |
| dc.identifier.email | Cheung, WS: wscheung@hku.hk | - |
| dc.identifier.authority | Cheung, WS=rp00678 | - |
| dc.description.nature | published_or_final_version | - |
| dc.identifier.doi | 10.1216/rmj.2020.50.2011 | - |
| dc.identifier.scopus | eid_2-s2.0-85099634750 | - |
| dc.identifier.hkuros | 322412 | - |
| dc.identifier.volume | 50 | - |
| dc.identifier.issue | 6 | - |
| dc.identifier.spage | 2011 | - |
| dc.identifier.epage | 2021 | - |
| dc.identifier.isi | WOS:000605471700008 | - |
| dc.publisher.place | United States | - |