On Hilbert’s Integral Inequality and Its Applications ()
Abstract
The main result of this paper is presented as follows Let h is homogeneous and symmetric of degree and Then
where
provided the integrals on the RHS do exists. Some other special cases are also deduced
Share and Cite:
Sulaiman, W. (2011) On Hilbert’s Integral Inequality and Its Applications.
Applied Mathematics,
2, 379-382. doi:
10.4236/am.2011.23045.
Conflicts of Interest
The authors declare no conflicts of interest.
References
[1]
|
G. H. Hardy, J. E. Littlewood and G. Polya, “Inequalities,” Cambridge University Press, Cambridge, 1952.
|
[2]
|
J. E. Mitronovic, J. E. Pecaric and A. M. Fink, “Inequalities Involving Functions and Their Integrals and Derivatives,” Boston Kluwer Academic Publishers, 1991.
|
[3]
|
P. X. Ying and G. Mingzhe, “On Hilbert’s Integral Inequality and Its Applications,” Journal of Applied Mathematics, Preprint.
|