On a Few Equivalent Statements of a Hilbert-Type Integral Inequality in the Whole Plane with the Hurwitz Zeta Function

2019 ◽  
pp. 319-352
Author(s):  
Themistocles M. Rassias ◽  
Bicheng Yang
Keyword(s):  
Zeta Function ◽  
Integral Inequality ◽  
Hurwitz Zeta Function ◽  
Type Integral ◽  
Hilbert Type

scholarly journals A reverse Hardy–Hilbert-type integral inequality involving one derivative function

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Qian Chen ◽  
Bicheng Yang
Keyword(s):  
Integral Inequality ◽  
Beta Function ◽  
Equivalent Form ◽  
Constant Factor ◽  
Weight Functions ◽  
Derivative Function ◽  
The Best Possible Constant ◽  
Type Integral ◽  
Hilbert Type ◽  
Hilbert Integral

AbstractIn this article, by using weight functions, the idea of introducing parameters, the reverse extended Hardy–Hilbert integral inequality and the techniques of real analysis, a reverse Hardy–Hilbert-type integral inequality involving one derivative function and the beta function is obtained. The equivalent statements of the best possible constant factor related to several parameters are considered. The equivalent form, the cases of non-homogeneous kernel and some particular inequalities are also presented.

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