A NOTE ON HILBERT TYPE INEQUALITY

Authors

  • B. G. PACHPATTE Department of Mathematics, Marathwada University, Aurangabad 431 004, Maharashtra In­dia.

DOI:

https://doi.org/10.5556/j.tkjm.29.1998.4258

Keywords:

Hilbert type ineqaulity, sequences of real numbers, integral analogue, Schwarz inequality, Jensen's inequality

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.

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.

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Published

1998-12-01

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

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Papers