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›› 2016, Vol. 33 ›› Issue (5): 584-589.DOI: 10.7523/j.issn.2095-6134.2016.05.002

• Research Articles • Previous Articles     Next Articles

A multi-parameter Hilbert-type integral inequality related to special functions

HUANG Lin1, LIU Qiong2   

  1. 1 Preparatory Department of Junior Education, Changsha Normal University, Changsha 410100, China;
    2 Department of Science and Information, Shaoyang University, Shaoyang 422000, Hunan, China
  • Received:2016-01-08 Revised:2016-03-26 Online:2016-09-15

Abstract:

By using the method of weight function and the techniques of real analysis and functional analysis and by introducing some special functions to jointly score the constant factor, a Hilbert-type integral inequality with multi-parameters is given. Its equivalent form is considered, and their constant factor is proved to be the best. Some meaningful results are obtained by choosing the special parameter values.

Key words: Hilbert-type integral inequality, weight function, the best constant factor, special function

CLC Number: