A New Hilbert-type integral inequality with a non-homogeneous kernel and its extension

 
 
 
  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract


    By introducing some parameters , using the weight function and the technique of real analysis, a new  Hilbert-type integral inequality with a non-homogeneous kernel as \(\frac{1}{|1-axy|^{\lambda_2}}(a\geq1)\) and its equivalent form are established. As application, the constant factor on the plane is the best value and its extension form with some parameters is also considered.

  • Keywords


    Some parameters; Hilbert-Type Integral Inequality; Best value; Extension.

  • References


      [1] Hardy GH.Note on a Theorem of H ilbert Concern ing Series of Positive Terms [J]. Proc London Math Soc,1925,23 (2):XLV-XLVL.

      [2] Hardy GH,Littewood JE,PolyaG.Inequalities[M].Cambridge:Cambridge University Press,1952.

      [3] Mitrinovic DS, Pecaric J, Fink AM. Inequalities Involving Functions and The ir Integrals and Derivatives [M ].Boston:Kluwer Academic Publishers, 1991.

      [4] Yongjing Li and Bing He. On inequalities of Hilbert's type [J].Bulletin of the Australian Mathematical Society,,2007,76(1):1-13.

      [5] Qiong Liu. A Hilbert-type Integral Inequality with Several Parameters J of Jinlin University: science edition, 2009, 47(5):903-908.

      [6] Bicheng Yang.On a Hilbert-type integral inequality with the homogeneous kernel of degree[J].J of Shanghai University(EnglEd):Natual Science,2010,14(6):391-395.

      [7] Weiliang Wu.A new Hilbert-type integral inequality with multiple independent parameters J of Lanzhou university of technology,2015,41 (1):160-163.

      [8] Jichang Kuang, Applied Inequalities, Shangdong Science Press, Jinan,2004.

      [9] Jichang Kuang, Introduction to real analysis, Hunan Education Press,Changsha,1996.


 

View

Download

Article ID: 5608
 
DOI: 10.14419/gjma.v4i3.5608




Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.