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A more accurate half-discrete Hardy-Hilbert-type inequality with the logarithmic function.
1Department of Mathematics, Guangdong University of Education, Xingang Zhonglu 351, Guangzhou, 510303 P.R. China.
Journal of Inequalities and Applications
|July 18, 2017
Summary
Researchers developed a more accurate half-discrete Hardy-Hilbert inequality using real analysis techniques. This inequality features a logarithmic kernel and an optimal constant factor, with further analysis of its properties.
Area of Science:
- Mathematical Analysis
- Inequalities
Background:
- Hardy-Hilbert-type inequalities are fundamental in analysis.
- Existing inequalities have limitations in accuracy and scope.
- Logarithmic kernels present unique analytical challenges.
Purpose of the Study:
- To derive a more accurate half-discrete Hardy-Hilbert-type inequality.
- To investigate inequalities involving logarithmic kernels.
- To determine the best possible constant factor for the inequality.
Main Methods:
- Utilizing weight functions and real analysis techniques.
- Applying Hermite-Hadamard's inequality.
- Exploring equivalent forms and operator expressions.
Main Results:
- A novel half-discrete Hardy-Hilbert-type inequality was established.
- A best possible constant factor was identified.
- Equivalent forms, operator expressions, reverses, and particular cases were analyzed.
Conclusions:
- The derived inequality offers improved accuracy.
- The study provides a comprehensive analysis of the inequality and its properties.
- This work contributes to the theory of integral inequalities.
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