A New Hilbert-type Inequality with the Homogeneous Kernel of Degree -2 and with the Integral

By Zeng Zheng, R. Gandhi, Zi-tian Xie. 2014

77 citations recorded by the source corpus.

By using the weight functions and by means of Hadamard's inequality, we present a new Hilbert-type inequality with the integral in whole plane, a best constant factor and a homogeneous kernel of degree-2 .

Subfields: Applied Mathematics, Geometry and Topology, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/62a780f0a56541c09fdaa8749443c484e310b0b2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Michael Th. Rassias
2. Bicheng Yang
3. Bing He
4. Yongjin Li

In Geometry and Topology

1. Michael Th. Rassias
2. Bicheng Yang

In Management Science and Operations Research

1. Michael Th. Rassias
2. Bicheng Yang

Citations in the corpus

• A Hilbert-Type Integral Inequality in the Whole Plane Related to the Hypergeometric Function and the Beta Function (2015, methodology): “< kλ Z ∞ −∞ |x|p(1−λ2)−1 f p(x)dx 1 p Z ∞ −∞ |y|q(1−λ2)−1gq(y)dy 1 q , (1.3) where the constant factor kλ=B( λ 2 , λ 2 )+2B(1−λ, λ 2 ) is still the best possible. Furthermore, Yang et al. [19]-[28] proved as well some new Hilbert-type integral inequalities in the whole plane. In this paper, using”