A New Generalization of Hardy-Hilbert'S Inequality


  • Birla Institute of Technology, Department of Mathematics, Ranchi, India
  • Indian Institute of Technology, SAG, Metcalfe House, Kharagpur, India


In this paper we generalize the Hardy-Hilbert's inequality by using generalized Holder's inequality. Some applications are also studied.


Hardy-Hilbert's Inequality, Holder's Inequality.

Subject Discipline

Mathematical Sciences

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G. Das and S. Nanda, Absolute almost convergence, Indian J. Maths., 34 (1992), 99–110.

G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, Cambridge University Press, Cambridge, MA , 1952.

I. J. Maddox, Elements of Functional Analysis, Cambridge University Press, Cambridge, MA, 1970.

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

S. Simmons, The sequence spaces l(pγ) and m(pv), Proc. London Math. Soc., 13 (1965), 422–436.

B. Yang, A refinement of more profound Hardy-Hilbert’s inequality, Hunan Ann. Math. 17, No.2 (1997), 35–38.

B. Yang, A refinement of Hilbert’s inequality, Huanghuai J. 13, No.2 (1997), 47–51.

B. Yang and L. Debnath, On a new generalization of Hardy-Hilbert’s inequality and its applications, J. Math. Anal. Appl. 233 (1999), 484–497.

B. Yang, On generalizations of Hardy-Hilbert’s integral inequalities, Acta Math. Sinica 41, No. 4 (1998), 839–844.


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