A Hilbert-type fractal integral inequality and its applications

Liu Qiong, Wenbing Sun

Type: Article

Publication Date: 2017-04-21

Citations: 15

DOI: https://doi.org/10.1186/s13660-017-1360-9

Abstract

By using thefractal theory and the methods of weight function, a Hilbert-type fractal integral inequality and its equivalent form are given. Their constant factors are proved being the best possible, and their applications are discussed briefly.

Locations

PubMed Central - View
Europe PMC (PubMed Central) - View - PDF
PubMed - View
Journal of Inequalities and Applications - View - PDF

Similar Works

Action	Title	Year	Authors
+	A Hilbert-type integral inequality on the fractal space	2017	Liu Qiong Dazhao Chen
+	A Hilbert-type Integral Inequality and Its Reverse	2008	Chuanli Wang
+	A New Hilbert-type Inequality and its Extension	2007	Qiliang Huang
+	A New Hilbert-type Integral Inequality and Its Reverse	2011	Guang Chen
+	A New Hilbert's Type Integral Inequality	2011	Ding Xuan-hao
+	A NEW HILBERT-TYPE INTEGRAL INEQUALITY AND ITS REVERSE	2007	Xie Zi-tian Zheng Zeng
+	AN EXTENSION OF THE HILBERT’S TYPE INTEGRAL INEQUALITY AND ITS APPLICATIONS	2007	Yang Bi-cheng
+	A New Hilbert-type Integral Inequality	2007	Wang Ai-zhen
+	A New Hilbert-type Integral Inequality	2009	WU Wei-liang
+	A Relation to Hilbert’s Integral Inequality and a Basic Hilbert-Type Inequality	2011	Bicheng Yang Themistocles M. Rassias
+	A Hilbert-type Integral Inequality on the Finite Interval	2009	Yang Bi-cheng
+	A New Hilbert-type Integral Inequality and Its Generalization	2005	Yang Bi-cheng
+	A New Hilbert-type Integral Inequality With Some Parameters and Its Reverses	2011	Liu Qiong
+	A Hilbert-type integral inequality.	2007	Yang Bi-cheng
+	A Hilbert-type integral inequality and the reverse forms.	2009	Wang Ai-zhen
+	A New Hilbert-Type Integral Inequality with Some Parameters and Its Reverses	2012	Liu Qiong
+ PDF Chat	On a Relation to Hilbert's Integral Inequality and a Hilbert-Type Inequality	2009	Bicheng Yang
+	A New Hilbert-Type Inequality	2011	Xie Zi-tian
+	A Hilbert-Type Local Fractional Integral Inequality with the Kernel of a Hyperbolic Cosecant Function	2023	Yingdi Liu Liu Qiong
+	A New Hilbert-type Integral Inequality with a Parameter	2007	GE Xiao-kui

Works That Cite This (14)

Action	Title	Year	Authors
+	On a mixed Kernel Hilbert‐type integral inequality and its operator expressions with norm	2020	Liu Qiong
+ PDF Chat	On Some New Dynamic Hilbert-Type Inequalities across Time Scales	2024	Mohammed Zakarya Ahmed I. Saied Amirah Ayidh I Al-Thaqfan Maha Ali Haytham M. Rezk
+ PDF Chat	A non-differentiable solution for the local fractional telegraph equation	2017	Jie Li Ce Zhang Weixing Liu Yuzhu Zhang Aimin Yang Ling Zhang
+ PDF Chat	Corrected Dual-Simpson-Type Inequalities for Differentiable Generalized Convex Functions on Fractal Set	2022	Abdelghani Lakhdari Wedad Saleh Badreddine Meftah Akhlad Iqbal
+	Multidimensional Hilbert-Type Inequalities Obtained via Local Fractional Calculus	2020	Mario Krnić Predrag Vuković
+ PDF Chat	Some Local Fractional Hilbert-Type Inequalities	2023	Predrag Vuković
+	THE STRUCTURAL FEATURES OF HILBERT-TYPE LOCAL FRACTIONAL INTEGRAL INEQUALITIES WITH ABSTRACT HOMOGENEOUS KERNEL AND ITS APPLICATIONS	2020	Yingdi Liu Liu Qiong
+	Exact Travelling Wave Solutions for Local Fractional Partial Differential Equations in Mathematical Physics	2018	Xiao‐Jun Yang Feng Gao J. A. Tenreiro Machado Dumitru Băleanu
+	Advanced Analysis of Local Fractional Calculus Applied to the Rice Theory in Fractal Fracture Mechanics	2021	Xiao‐Jun Yang Dumitru Băleanu H. M. Srivastava
+	A class of fractal Hilbert‐type inequalities obtained via Cantor‐type spherical coordinates	2021	Dumitru Băleanu Mario Krnić Predrag Vuković

Works Cited by This (8)

Action	Title	Year	Authors
+	Advanced Local Fractional Calculus and Its Applications	2012	Xiao‐Jun Yang
+	Inequalities Involving Functions and Their Integrals and Derivatives	1991	D. S. Mitrinović ‎Josip Pečarić A. M. Fink
+ PDF Chat	Analysis of Fractal Wave Equations by Local Fractional Fourier Series Method	2013	Yong-Ju Yang Dumitru Băleanu Xiao‐Jun Yang
+ PDF Chat	Generalized Convex Functions on Fractal Sets and Two Related Inequalities	2014	Huixia Mo Xin Sui Dongyan Yu
+ PDF Chat	Generalizations of Hölder’s and Some Related Integral Inequalities on Fractal Space	2013	Guang-Sheng Chen
+	ON THE EXTENDED HILBERT'S INTEGRAL INEQUALITY	2004	Bicheng Yang
+	Generalized Pompeiu type inequalities for local fractional integrals and its applications	2015	Samet Erden Mehmet Zeki Sarıkaya
+	An Introduction to Special Functions	2016	Carlo Viola