Affiliation:
1. School of Mathematics, Guangdong University of Education , Guangzhou , Guangdong 510303 , P. R. China
Abstract
Abstract
In this article, a new reverse half-discrete Hilbert-type inequality with one partial sum involving one derivative function of higher order is obtained, by using the weight functions, the mid-value theorem, and the techniques of real analysis. A few equivalent statements of the best possible constant factor related to several parameters are considered. As applications, the equivalent forms and some particular inequalities are provided.
Reference19 articles.
1. G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge University Press, Cambridge, 1934.
2. M. Krnić and J. Pečarić, Extension of Hilbert’s inequality, J. Math. Anal. Appl. 324 (2006), no. 1, 150–160.
3. B. C. Yang, On a generalization of Hilbert double series theorem, Math. Inequal. Appl. 5 (2002), no. 2, 197–204.
4. M. Th. Rassias and B. C. Yang, On half-discrete Hilbert’s inequality, Appl. Math. Comput. 220 (2013), 75–93.
5. B. C. Yang and L. Debnath, Half-discrete Hilbert-type Inequalities, World Scientific Pub. Co., Singapore, 2014.