Hilbert型级数不等式的研究进展及应用

Abstract

Abstract: Through the analysis of the research characteristics of Hilbert-type series inequalities in each stage, we analyzed and summarized
the development process and the current status of research of Hilbert-type series inequalities from simple to deep, from special to general, from homogeneous kernel to non-homogeneous kernel and from low dimension to high dimension, and gave some of the latest research results.

Key words: Hilbert-type series inequality, research progress, current status of research, theoretical system, weigh function method, series operator

CLC Number:

O178

HONG Yong, CHEN Qiang. Research Progress and Applications of Hilbert-Type Series Inequalities [J].Journal of Jilin University Science Edition, 2021, 59(5): 1131-1140.

[1]	HONG Yong, WU Chunyang, CHEN Qiang. Matching Parameter Conditions for the Best Hilbert-Type Integral Inequality with a Class of Non-homogeneous Kernels [J]. Journal of Jilin University Science Edition, 2021, 59(2): 207-212.
[2]	HONG Yong, ZENG Zhihong. Necessary and Sufficient Condition for Establishmentof HalfDiscrete HilbertType Inequality with Kernel G(n^λ1/x^λ2)(λ₁λ₂>0) and Its Application#br# [J]. Journal of Jilin University Science Edition, 2020, 58(3): 507-512.
[3]	XIN Dongmei, YANG Bicheng. A HalfDiscrete HilbertType Inequality of More Accurate Strengthened Version [J]. Journal of Jilin University Science Edition, 2020, 58(2): 225-230.
[4]	QIU Ke’e, CHEN Songliang, DENG Xicai, TAO Lei, LIU Zhuo. A Class of Inequalities of Hadamard with Local Fractional Integrals for Generalized s-Convex Functions on Fractal Sets and Their Applications#br# [J]. Journal of Jilin University Science Edition, 2019, 57(04): 793-802.
[5]	SUN Wenbing. Hadamard Type Fractional Integral Inequalities withParameter for Harmonically Quasiconvex Functions [J]. Journal of Jilin University Science Edition, 2019, 57(04): 803-808.
[6]	HONG Yong. Equivalent Condition for Obtaining the Best Constant Factorof HilbertType Multiple Series Inequalities with Homogeneous Kernel and Applications#br# [J]. Journal of Jilin University Science Edition, 2019, 57(2): 191-198.
[7]	LIU Qiong. HilbertType Integral Inequality Related to Some SpecialFunctions and Its Operator Expressions with Norm#br# [J]. Journal of Jilin University Science Edition, 2018, 56(6): 1359-1365.
[8]	SUN Wenbing. Generalized Harmonically s-Convex Functions andHadamard Type Inequalities on Fractal Sets#br# [J]. Journal of Jilin University Science Edition, 2018, 56(6): 1366-1372.
[9]	YANG Bicheng, WANG Aizhen. A Hilbert’s Integral Inequality in the Whole Planewith Non-homogeneous Kernel [J]. Journal of Jilin University Science Edition, 2018, 56(4): 819-824.
[10]	HONG Yong, ZENG Zhihong. Necessary and Sufficient Condition for Establishment ofHilbertType Series Inequality with a Class ofQuasihomogeneous Kernels and Its Application [J]. Journal of Jilin University Science Edition, 2018, 56(3): 530-536.
[11]	HONG Yong, WEN Yamin. Necessary and Sufficient Condition for a Class of HilbertType IntegralInequality with a Nonhomogeneous Kernel and Its Application [J]. Journal of Jilin University Science Edition, 2018, 56(2): 227-232.
[12]	YANG Jingmei, LI Zunfeng, YANG Heju. Nonlinear Boundary Value Problem for Generalized Hypermonogenic Function Vector in Clifford Analysis [J]. Journal of Jilin University Science Edition, 2018, 56(1): 28-34.
[13]	YANG Bicheng, CHEN Qiang. Equivalent Conditions of Existence of a Class of Reverse HardyType Integral Inequalities with Nonhomogeneous Kernel [J]. Journal of Jilin University Science Edition, 2017, 55(04): 804-808.
[14]	SUN Wenbing. HadamardType Inequalities with Mapping Derivatives Being sConvex Functions and under Fractional Integrals [J]. Journal of Jilin University Science Edition, 2017, 55(04): 809-814.
[15]	GU Zhaohui, YANG Bicheng. A HilbertType Integral Inequality in Whole PlaneRelated to Gamma Function of Best Constant Factor [J]. Journal of Jilin University Science Edition, 2017, 55(03): 513-518.

Research Progress and Applications of Hilbert-Type Series Inequalities

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