A Hilbert-type integral inequality under configuring free power and its applications

Liu, Qiong

doi:10.1186/s13660-019-2039-1

Cited by 13 publications

(7 citation statements)

References 11 publications

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“…In 2017, Hong [18] proved an equivalent condition between (3) and a few parameters. Some similar results were obtained in [19][20][21][22][23][24][25][26][27][28].…”

Section: Introductionsupporting

confidence: 82%

Equivalent Properties of Two Kinds of Hardy-Type Integral Inequalities

2021

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In this paper, using weight functions as well as employing various techniques from real analysis, we establish a few equivalent conditions of two kinds of Hardy-type integral inequalities with nonhomogeneous kernel. To prove our results, we also deduce a few equivalent conditions of two kinds of Hardy-type integral inequalities with a homogeneous kernel in the form of applications. We additionally consider operator expressions. Analytic inequalities of this nature and especially the techniques involved have far reaching applications in various areas in which symmetry plays a prominent role, including aspects of physics and engineering.

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“…In 2017, Hong [18] proved an equivalent condition between (3) and a few parameters. Some similar results were obtained in [19][20][21][22][23][24][25][26][27][28].…”

Section: Introductionsupporting

confidence: 82%

Equivalent Properties of Two Kinds of Hardy-Type Integral Inequalities

2021

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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][22][23][24][25]. In this paper, by introducing the parameters 1 , 2 , 3 , 4 , the basic kernels k 1 (x, ) = 1 x+ , k 2 (x, ) =…”

Section: Liumentioning

confidence: 99%

“…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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“…In 2013, Yang [25] also studied the equivalence of ( 6) and (7) by adding a condition h(u) = k λ (u, 1). In 2017, Hong [9] studied an equivalent condition for (6) involving certain parameters, and some further related results were established in [4], [5], [15], [29], [28].…”

Section: Introductionmentioning

confidence: 99%

An equivalent property of a Hilbert-type integral inequality and its applications

Yang

Andrica

Bagdasar

et al. 2022

APPL ANAL DISCRETE M

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Making use of complex analytic techniques as well as methods involving weight functions, we study a few equivalent conditions of a Hilbert-type integral inequality with nonhomogeneous kernel and parameters. In the form of applications we deduce a few equivalent conditions of a Hilbert-type integral inequality with homogeneous kernel, and we additionally consider operator expressions.

show abstract

A Hilbert-type integral inequality under configuring free power and its applications

Cited by 13 publications

References 11 publications

Equivalent Properties of Two Kinds of Hardy-Type Integral Inequalities

Equivalent Properties of Two Kinds of Hardy-Type Integral Inequalities

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

An equivalent property of a Hilbert-type integral inequality and its applications

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