A Half-Discrete Hardy-Hilbert-Type Inequality with a Best Possible Constant Factor Related to the Hurwitz Zeta Function

Rassias, Michael Th.; Yang, Bicheng

doi:10.1007/978-3-319-49242-1_10

Cited by 3 publications

(2 citation statements)

References 17 publications

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“…The research of Hilbert‐type integral inequalities with hybrid kernels is one of the important contents too. The so‐called hybrid kernel research is to combine some basic kernels into new integral kernels and do the corresponding research works, which began in 2008 and yielded a lot of results (see previous studies 21‐25 ). In this paper, by introducing the parameters λ 1 , λ 2 , λ 3 , λ 4 , the basic kernels

k_{1} false(x, y false) = \frac{1}{x + y}, k_{2} false(x, y false) = \frac{(||, \ln \frac{y}{x})}{x + y}, k_{3} false(x, y false) = \max false{x, y false}, k_{4} false(x, y false) = \min false{x, y false}

are parametric combined to a mixed kernel as

k false(x, y false) : = \frac{{(||, \ln \frac{y}{x})}^{λ_{1}} {false(\min false{x, y false} false)}^{λ_{2}}}{{false(x + y false)}^{λ_{3}} {false(\max false{x, y false} false)}^{λ_{4}}}

.…”

Section: Introductionmentioning

confidence: 99%

On a mixed Kernel Hilbert‐type integral inequality and its operator expressions with norm

Liu

2020

Math Methods in App Sciences

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By using some real analysis techniques, we study the structural characteristics of a multi-parameter Hilbert-type integral inequality with the hybrid kernel and obtain some equivalent conditions for this inequality. We also consider the operator expression of the equivalent inequalities. The conclusions not only integrate some results of references but also find some new Hilbert-type integral inequalities with simple form by choosing suitable parameter values.

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k_{1} false(x, y false) = \frac{1}{x + y}, k_{2} false(x, y false) = \frac{(||, \ln \frac{y}{x})}{x + y}, k_{3} false(x, y false) = \max false{x, y false}, k_{4} false(x, y false) = \min false{x, y false}

are parametric combined to a mixed kernel as

k false(x, y false) : = \frac{{(||, \ln \frac{y}{x})}^{λ_{1}} {false(\min false{x, y false} false)}^{λ_{2}}}{{false(x + y false)}^{λ_{3}} {false(\max false{x, y false} false)}^{λ_{4}}}

.…”

Section: Introductionmentioning

confidence: 99%

On a mixed Kernel Hilbert‐type integral inequality and its operator expressions with norm

Liu

2020

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…In [8][9][10], Yang et al established some important extensions of a Hardy-Hilbert-type inequality by using the weight coefficient method and techniques of real analysis.…”

Section: Introductionmentioning

confidence: 99%