Sharp Estimation Type Inequalities for Lipschitzian Mappings in Euclidean Sense on a Disk
Some sharp trapezoid and midpoint type inequalities for Lipschitzian bifunctions defined on a closed disk in Euclidean sense are obtained by the use of polar coordinates. Also, bifunctions whose partial derivative is Lipschitzian are considered. A new presentation of Hermite-Hadamard inequality for...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/6615626 |
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| _version_ | 1850237683956187136 |
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| author | M. Rostamian Delavar S. S. Dragomir M. De La Sen |
| author_facet | M. Rostamian Delavar S. S. Dragomir M. De La Sen |
| author_sort | M. Rostamian Delavar |
| collection | DOAJ |
| description | Some sharp trapezoid and midpoint type inequalities for Lipschitzian bifunctions defined on a closed disk in Euclidean sense are obtained by the use of polar coordinates. Also, bifunctions whose partial derivative is Lipschitzian are considered. A new presentation of Hermite-Hadamard inequality for convex function defined on a closed disk and its reverse are given. Furthermore, two mappings Ht and ht are considered to give some generalized Hermite-Hadamard type inequalities in the case that considered functions are Lipschitzian in Euclidean sense on a disk. |
| format | Article |
| id | doaj-art-13cc7c61072b41d4945bf4c8cf3075dc |
| institution | OA Journals |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-13cc7c61072b41d4945bf4c8cf3075dc2025-08-20T02:01:41ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/66156266615626Sharp Estimation Type Inequalities for Lipschitzian Mappings in Euclidean Sense on a DiskM. Rostamian Delavar0S. S. Dragomir1M. De La Sen2Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, P. O. Box 1339, Bojnord 94531, IranMathematics, College of Engineering & Science, Victoria University, PO Box 14428, Melbourne City, MC 8001, AustraliaInstitute of Research and Development of Processes, University of Basque Country, Campus of Leioa (Bizkaia)-Aptdo. 644-Bilbao, Bilbao 48080, SpainSome sharp trapezoid and midpoint type inequalities for Lipschitzian bifunctions defined on a closed disk in Euclidean sense are obtained by the use of polar coordinates. Also, bifunctions whose partial derivative is Lipschitzian are considered. A new presentation of Hermite-Hadamard inequality for convex function defined on a closed disk and its reverse are given. Furthermore, two mappings Ht and ht are considered to give some generalized Hermite-Hadamard type inequalities in the case that considered functions are Lipschitzian in Euclidean sense on a disk.http://dx.doi.org/10.1155/2021/6615626 |
| spellingShingle | M. Rostamian Delavar S. S. Dragomir M. De La Sen Sharp Estimation Type Inequalities for Lipschitzian Mappings in Euclidean Sense on a Disk Journal of Function Spaces |
| title | Sharp Estimation Type Inequalities for Lipschitzian Mappings in Euclidean Sense on a Disk |
| title_full | Sharp Estimation Type Inequalities for Lipschitzian Mappings in Euclidean Sense on a Disk |
| title_fullStr | Sharp Estimation Type Inequalities for Lipschitzian Mappings in Euclidean Sense on a Disk |
| title_full_unstemmed | Sharp Estimation Type Inequalities for Lipschitzian Mappings in Euclidean Sense on a Disk |
| title_short | Sharp Estimation Type Inequalities for Lipschitzian Mappings in Euclidean Sense on a Disk |
| title_sort | sharp estimation type inequalities for lipschitzian mappings in euclidean sense on a disk |
| url | http://dx.doi.org/10.1155/2021/6615626 |
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