Results 11 to 20 of about 380,648 (224)

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

, 2017
Using methods of weight functions, techniques of real analysis as well as the Hermite-Hadamard inequality, a half-discrete Hardy-Hilbert-type inequality with multi-parameters and a best possible constant factor related to the Hurwitz zeta function and the Riemann zeta function is obtained.
Rassias, Michael Th., Yan, Bicheng
openaire   +2 more sources

Equivalent property of a half-discrete Hilbert’s inequality with parameters

Journal of Inequalities and Applications, 2018
By using the weight functions and the idea of introducing parameters, a half-discrete Hilbert inequality with a nonhomogeneous kernel and its equivalent form are given.
Zhenxiao Huang, Bicheng Yang
doaj   +1 more source

On an Extension of a Hardy–Hilbert-Type Inequality with Multi-Parameters

Mathematics, 2021
Making use of weight coefficients as well as real/complex analytic methods, an extension of a Hardy–Hilbert-type inequality with a best possible constant factor and multiparameters is established.
Bicheng Yang, Michael Th. Rassias, Andrei Raigorodskii   +2 more
doaj   +1 more source

The necessary and sufficient conditions for the existence of a kind of Hilbert-type multiple integral inequality with the non-homogeneous kernel and its applications

Journal of Inequalities and Applications, 2017
For x = ( x 1 , … , x n ) ${x}= ( {x}_{1},\ldots, {x}_{{n}} )$ , u ( x ) = ( ∑ i = 1 n a i x i ρ ) 1 / ρ ${u} ( {x} ) = ( \sum_{{i}=1}^{{n}} {a}_{{i}} {x}_{{i}}^{\rho} )^{1/\rho}$ , v ( y ) = ( ∑ i = 1 n b i y i ρ ) 1 / ρ ${v} ( {y} ) = ( \sum_{{i}=1 ...
Yong Hong, Qiliang Huang, Bicheng Yang, Jianquan Liao   +3 more
doaj   +1 more source

A reverse Mulholland-type inequality in the whole plane

Journal of Inequalities and Applications, 2018
We present a new reverse Mulholland-type inequality in the whole plane with a best possible constant factor by introducing multiparameters, applying weight coefficients, and using the Hermite–Hadamard inequality.
Jianquan Liao, Bicheng Yang
doaj   +1 more source

A More Accurate Half-Discrete Hardy-Hilbert-Type Inequality with the Best Possible Constant Factor Related to the Extended Riemann-Zeta Function

, 2015
By the method of weight coefficients, techniques of real analysis and Hermite-Hadamard's inequality, a half-discrete Hardy-Hilbert-type inequality related to the kernel of the hyperbolic cosecant function with the best possible constant factor expressed in terms of the extended Riemann-zeta function is proved.
Rassias, Michael Th., Yang, Bicheng
openaire   +2 more sources

An extended reverse Hardy–Hilbert’s inequality in the whole plane

Journal of Inequalities and Applications, 2018
Using weight coefficients, a complex integral formula, and Hermite–Hadamard’s inequality, we give an extended reverse Hardy–Hilbert’s inequality in the whole plane with multiparameters and a best possible constant factor.
Qiang Chen, Bicheng Yang
doaj   +1 more source

A New Reverse Extended Hardy–Hilbert’s Inequality with Two Partial Sums and Parameters

Axioms, 2023
By using the methods of real analysis and the mid-value theorem, we introduce some lemmas and obtain a new reverse extended Hardy–Hilbert’s inequality with two partial sums and multi-parameters.
Jianquan Liao, Bicheng Yang
doaj   +1 more source

On a Discrete Version of the Hardy–Littlewood–Polya Inequality Involving Multiple Parameters in the Whole Plane

Mathematics
In this paper, by introducing multiple parameters, we establish a discrete version of the Hardy–Littlewood–Polya inequality in the whole plane. For the obtained inequality, we give the equivalent statements of the best possible constant factor linked to ...
Bicheng Yang, Shanhe Wu
doaj   +1 more source

On a reverse Mulholland’s inequality in the whole plane

Journal of Inequalities and Applications, 2018
By introducing multi-parameters, applying the weight coefficients and Hermite–Hadamard’s inequality, we give a reverse of the extended Mulholland inequality in the whole plane with the best possible constant factor.
Aizhen Wang, Bicheng Yang
doaj   +1 more source