Parameterized Hilbert-Type Integral Inequalities in the Whole Plane
By the use of the way of real analysis, we estimate the weight functions and give some new Hilbert-type integral inequalities in the whole plane with nonhomogeneous kernels and multiparameters. The constant factors related to the hypergeometric function and the beta function are proved to be the bes...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/169061 |
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| _version_ | 1832566583086546944 |
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| author | Qiliang Huang Shanhe Wu Bicheng Yang |
| author_facet | Qiliang Huang Shanhe Wu Bicheng Yang |
| author_sort | Qiliang Huang |
| collection | DOAJ |
| description | By the use of the way of real analysis, we estimate the weight functions and give
some new Hilbert-type integral inequalities in the whole plane with nonhomogeneous
kernels and multiparameters. The constant factors related to the hypergeometric function
and the beta function are proved to be the best possible. We also consider the
equivalent forms, the reverses, and some particular cases in the homogeneous kernels. |
| format | Article |
| id | doaj-art-f25e750b6b2549e991d48238fa0cc5e7 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-f25e750b6b2549e991d48238fa0cc5e72025-02-03T01:03:51ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/169061169061Parameterized Hilbert-Type Integral Inequalities in the Whole PlaneQiliang Huang0Shanhe Wu1Bicheng Yang2Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, ChinaDepartment of Mathematics and Computer Science, Longyan University, Longyan, Fujian 364012, ChinaDepartment of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, ChinaBy the use of the way of real analysis, we estimate the weight functions and give some new Hilbert-type integral inequalities in the whole plane with nonhomogeneous kernels and multiparameters. The constant factors related to the hypergeometric function and the beta function are proved to be the best possible. We also consider the equivalent forms, the reverses, and some particular cases in the homogeneous kernels.http://dx.doi.org/10.1155/2014/169061 |
| spellingShingle | Qiliang Huang Shanhe Wu Bicheng Yang Parameterized Hilbert-Type Integral Inequalities in the Whole Plane The Scientific World Journal |
| title | Parameterized Hilbert-Type Integral Inequalities in the Whole Plane |
| title_full | Parameterized Hilbert-Type Integral Inequalities in the Whole Plane |
| title_fullStr | Parameterized Hilbert-Type Integral Inequalities in the Whole Plane |
| title_full_unstemmed | Parameterized Hilbert-Type Integral Inequalities in the Whole Plane |
| title_short | Parameterized Hilbert-Type Integral Inequalities in the Whole Plane |
| title_sort | parameterized hilbert type integral inequalities in the whole plane |
| url | http://dx.doi.org/10.1155/2014/169061 |
| work_keys_str_mv | AT qilianghuang parameterizedhilberttypeintegralinequalitiesinthewholeplane AT shanhewu parameterizedhilberttypeintegralinequalitiesinthewholeplane AT bichengyang parameterizedhilberttypeintegralinequalitiesinthewholeplane |