A NOTE ON HILBERT TYPE INEQUALITY

Main Article Content

B. G. PACHPATTE

Abstract




In the present note we establish a new Hilbert type inequality mvolving sequences of real numbers. An integral analogue of the main result is also given.




Article Details

How to Cite
PACHPATTE, B. G. (1998). A NOTE ON HILBERT TYPE INEQUALITY. Tamkang Journal of Mathematics, 29(4), 293–298. https://doi.org/10.5556/j.tkjm.29.1998.4258
Section
Papers

References

Y. C. Chow, "On inequalities of Hilbert and Widder," J. London Math. Soc., 14 (1939), 151 - 1 54 .

G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, Cambridge University Press, 1934.

V. Levin, "On the two parameter·extension and analogue of Hilbert's inequality," J. London Math. Soc., 11 (1936), 119-124.

G. Mingzhe, "An improvement of Hardy-Riesz's extension of the Hilbert inequality," J. Math. Res. Exposition, 14 (1994), 255-259.

G. Mingzhe, "On Hilbert's inequality and its applications," J. Math. Anal. Appl., 212 (1997), 316-323.

D.S. Mitrinovic, Analytic Inequalities, Springer-Verlag, Berlin, New York, 1970.

D. S. Mitrinovit and J.E . Pecaric, "On inequahties of Hilbert and Widder," Proc. Edinburgh Math. Soc, 34 (1991), 411-414.

J. Nemeth, "Generalizations of the Hardy-Littlewood inequality," Acta Sci. Math., (Szeged) 32 (1971), 295-299.

B. G. Pachpatte, "A note on some series inequalities," Tamkang J. Math., 27 {1996), 77-79.

D. V. Widder, "An inequality related to one of Hilbert's," J. London Math. Soc., 4(1929), 194-198.