New inequalities similar to Hardy-Hilbert’s inequality

New inequalities similar to Hardy-Hilbert’s inequality

In this paper, we establish a new inequality similar to Hardy-Hilbert’s inequality. As applications, some particular results and the equivalent form are derived. The integral analogues of the main results are also given.

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  • [1] Hardy G.H., Littlewood J.E. and Polya G., Inequalities, Cambridge University Press, Cambrige, 1952.
  • [2] Krylov V. I., Approximation Calculation of Integrals, Macmillan, New York, 1962.
  • [3] Kuang J., Applied Inequalities, Shangdong Science and Technology Press, Jinan, 2004.
  • [4] Krnic M. and Pecaric J., Extension of Hilbert’s inequality, J. Math. Anal. Appl., 324,(2006), 150-160.
  • [5] Mitrinovic D.S., Analytic Inequalities, Springer-Verlag Berlin, New York, 1970.
  • [6] Mitrinovic D.S., Pecaric J.E. and Fink A.M., Inequalities Involving Functions and Their Integrals and Derivatives, Kluwer Academic Publishers, Boston, 1991.
  • [7] Pachpatte B.G., On some new inequalities similar to Hilbert’s inequality, J. Math. Anal. Appl., 226,(1998), 166- 179.
  • [8] Pachpatte B.G., Inequalities similar to certain extensions of Hilbert’s inequality, J. Math. Anal. Appl., 243,(2000), 217-227.
  • [9] Wang Z. and Guo D., An Introduction to Special Functions, Science Press, Beijing, 1979.
  • [10] Yang B. and Rassias T. M., On the way of weight coefficient and research for the Hilbert-type inequalities, Math. Ineq. Appl., 6(4)(2003), 625-658.