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A half-discrete Hilbert-type inequality in the whole plane with the constant factor related to a cotangent function.
- Source :
-
Journal of Inequalities & Applications . 3/24/2023, Vol. 2023 Issue 1, p1-15. 15p. - Publication Year :
- 2023
-
Abstract
- In this work, by the introduction of some parameters, a new half-discrete kernel function in the whole plane is defined, which involves both the homogeneous and the nonhomogeneous cases. By employing some techniques of real analysis, especially the method of a weight function, a new half-discrete Hilbert-type inequality with the new kernel function, as well as its equivalent Hardy-type inequalities are established. Moreover, it is proved that the constant factors of the newly obtained inequalities are the best possible. Finally, assigning special values to the parameters, some new half-discrete Hilbert-type inequalities with special kernels are presented at the end of the paper. [ABSTRACT FROM AUTHOR]
- Subjects :
- *COTANGENT function
*KERNEL functions
*INTEGRAL inequalities
Subjects
Details
- Language :
- English
- ISSN :
- 10255834
- Volume :
- 2023
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Inequalities & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 162680857
- Full Text :
- https://doi.org/10.1186/s13660-023-02951-z