On a Discrete Hilbert Type Inequality With Non–Homogeneous Kernel
DOI:
https://doi.org/10.5644/SJM.06.1.02Keywords:
Discrete Hilbert type inequality, Dirichlet–series, non–homogeneous kernel, homogeneous kernel, H¨older inequality, binomial expansion, beta functionAbstract
New extensions are given for the discrete Hilbert type inequality with non–homogeneous kernel. By this, recently published results by Pogány have been improved by a Hilbert type inequalities in homogeneous kernel case derived by Krnić and Pečarić. Mathematical tools also used are the Dirichlet series’ Laplace–integral representation and the classical Hölder inequality.
2000 Mathematics Subject Classification. Primary 26D15; Secondary 40B05, 40G99
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References
G. H. Hardy, J. E. Littlewood and Gy P´olya, Inequalities, Cambridge University Press, Cambridge, 1934.
M. Krni´c, M. Gao, J. Peˇcari´c and X. Gao, On the best constant in Hilbert’s inequality, Math. Ineq. Appl., 8 (2) (2005), 317-329.
M. Krni´c and J. Peˇcari´c, Extension of Hilbert’s inequality, Math. Anal. Appl., 324 (2006), 150–160.
T. K. Pog´any, Hilbert’s double series theorem extended to the case of non–homogeneous kernels, J. Math. Anal. Appl., 342 (2) (2008), 1485–1489.
T. K. Pog´any, H. M. Srivastava and Z. Tomovski, ˇ Some families of Mathieu a-series and alternating Mathieu a-series, Appl. Math. Comput., 173 (2006) 69–108.
