Recent Developments of Hilbert-Type Discrete and Integral Inequalities with Applications
This paper deals with recent developments of Hilbert-type discrete and integral inequalities by introducing kernels, weight functions, and multiparameters. Included are numerous generalizations, extensions, and refinements of Hilbert-type inequalities involving many special functions such as beta, g...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/871845 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832549359076507648 |
|---|---|
| author | Lokenath Debnath Bicheng Yang |
| author_facet | Lokenath Debnath Bicheng Yang |
| author_sort | Lokenath Debnath |
| collection | DOAJ |
| description | This paper deals with recent developments of Hilbert-type discrete and integral inequalities by introducing kernels, weight functions, and multiparameters. Included are numerous generalizations, extensions, and refinements of Hilbert-type inequalities involving many special functions such as beta, gamma, logarithm, trigonometric, hyper-bolic, Bernoulli's functions and Bernoulli's numbers, Euler's constant, zeta function, and hypergeometric functions with many applications. Special attention is given to many equivalent inequalities and to conditions under which the constant factors involved in inequalities are the best possible. Many particular cases of Hilbert-type inequalities are presented with numerous applications. A large number of major books and recent research papers published during 2009–2012 are included to stimulate new interest in future study and research. |
| format | Article |
| id | doaj-art-1d453eceafe64e3a801b951f36bac7dd |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-1d453eceafe64e3a801b951f36bac7dd2025-02-03T06:11:24ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/871845871845Recent Developments of Hilbert-Type Discrete and Integral Inequalities with ApplicationsLokenath Debnath0Bicheng Yang1Department of Mathematics, University of Texas-Pan American, Edinburg, TX 78539, USADepartment of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, ChinaThis paper deals with recent developments of Hilbert-type discrete and integral inequalities by introducing kernels, weight functions, and multiparameters. Included are numerous generalizations, extensions, and refinements of Hilbert-type inequalities involving many special functions such as beta, gamma, logarithm, trigonometric, hyper-bolic, Bernoulli's functions and Bernoulli's numbers, Euler's constant, zeta function, and hypergeometric functions with many applications. Special attention is given to many equivalent inequalities and to conditions under which the constant factors involved in inequalities are the best possible. Many particular cases of Hilbert-type inequalities are presented with numerous applications. A large number of major books and recent research papers published during 2009–2012 are included to stimulate new interest in future study and research.http://dx.doi.org/10.1155/2012/871845 |
| spellingShingle | Lokenath Debnath Bicheng Yang Recent Developments of Hilbert-Type Discrete and Integral Inequalities with Applications International Journal of Mathematics and Mathematical Sciences |
| title | Recent Developments of Hilbert-Type Discrete and Integral Inequalities with Applications |
| title_full | Recent Developments of Hilbert-Type Discrete and Integral Inequalities with Applications |
| title_fullStr | Recent Developments of Hilbert-Type Discrete and Integral Inequalities with Applications |
| title_full_unstemmed | Recent Developments of Hilbert-Type Discrete and Integral Inequalities with Applications |
| title_short | Recent Developments of Hilbert-Type Discrete and Integral Inequalities with Applications |
| title_sort | recent developments of hilbert type discrete and integral inequalities with applications |
| url | http://dx.doi.org/10.1155/2012/871845 |
| work_keys_str_mv | AT lokenathdebnath recentdevelopmentsofhilberttypediscreteandintegralinequalitieswithapplications AT bichengyang recentdevelopmentsofhilberttypediscreteandintegralinequalitieswithapplications |