scholarly journals Inequalities Similar to Hilbert's Inequality

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Chang-Jian Zhao
Keyword(s):  
Hilbert’S Inequality ◽  
New Inequalities

In the present paper, we establish some new inequalities similar to Hilbert’s type inequalities. Our results provide some new estimates to these types of inequalities.

Fractional Cesàro Matrix and its Associated Sequence Space

2021 ◽  
Vol 8 (1) ◽  
pp. 24-39
Author(s):  
H. Roopaei ◽  
M. İlkhan
Keyword(s):  
Sequence Space ◽  
Topological Properties ◽  
Hilbert’S Inequality ◽  
Hilbert Operator ◽  
Cesàro Matrix ◽  
New Inequalities

Abstract In this research, we introduce a new fractional Cesàro matrix and investigate the topological properties of the sequence space associated with this matrix.We also introduce a fractional Gamma matrix aswell and obtain some factorizations for the Hilbert operator based on Cesàro and Gamma matrices. The results of these factorizations are two new inequalities one ofwhich is a generalized version of thewell-known Hilbert’s inequality. There are also some challenging problems that authors share at the end of the manuscript and invite the researcher for trying to solve them.

scholarly journals On Further Analogs of Hilbert's Inequality

2007 ◽  
Vol 2007 ◽  
pp. 1-6 ◽  
Author(s):  
Yongjin Li ◽  
You Qian ◽  
Bing He
Keyword(s):  
Equivalent Form ◽  
Type Inequality ◽  
Hilbert’S Inequality ◽  
New Inequalities

By introducing the function|lnx−lny|/(x+y+|x−y|), we establish new inequalities similar to Hilbert's type inequality for integrals. As applications, we give its equivalent form as well.

scholarly journals INEQUALITIES SIMILAR TO THE INTEGRAL ANALOGUE OF HILBERT'S INEQUALITY

1999 ◽  
Vol 30 (2) ◽  
pp. 139-146
Author(s):  
B. G. PACHPATTE
Keyword(s):  
Hilbert’S Inequality ◽  
Elementary Analysis ◽  
Integral Analogue ◽  
New Inequalities

In the present paper we establish some new inequalities similar to the integral ana­logue of Hilbert's inequality by using a fairly elementary analysis.

scholarly journals On inequalities of Hilbert's type

2007 ◽  
Vol 76 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Yongjin Li ◽  
Bing He
Keyword(s):  
Integral Inequality ◽  
Equivalent Form ◽  
Type Inequality ◽  
Constant Factor ◽  
Best Constant ◽  
Hilbert’S Inequality ◽  
Type Integral ◽  
Best Constant Factor ◽  
Special Case ◽  
New Inequalities

By introducing the function 1/(min{x, y}), we establish several new inequalities similar to Hilbert's type inequality. Moreover, some further unification of Hardy-Hilbert's and Hardy-Hilbert's type integral inequality and its equivalent form with the best constant factor are proved, which contain the classic Hilbert's inequality as special case.

On an extension of the Hardy-Hilbert theorem

2005 ◽  
Vol 42 (1) ◽  
pp. 21-35 ◽  
Author(s):  
J. Weijian ◽  
G. Mingzhe ◽  
G. Xuemei
Keyword(s):  
Beta Function ◽  
Summation Formula ◽  
Hilbert’S Inequality ◽  
Two Parameters

A weighted Hardy-Hilbert’s inequality with the parameter λ of form \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\sum\limits_{m = 1}^\infty {\sum\limits_{n = 1}^\infty {\frac{{a_m b_n }}{{(m + n)^\lambda }}} < B^* (\lambda )\left( {\sum\limits_{n = 1}^\infty {n^{1 - \lambda } a_{a_n }^p } } \right)^{{1 \mathord{\left/ {\vphantom {1 p}} \right. \kern-\nulldelimiterspace} p}} \left( {\sum\limits_{n = 1}^\infty {n^{1 - \lambda } b_n^q } } \right)^q }$$ \end{document} is established by introducing two parameters s and λ, where \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\tfrac{1}{p} + \tfrac{1}{q} = 1,p \geqq q > 1,1 - \tfrac{q}{p} < \lambda \leqq 2,B^* (\lambda ) = B(\lambda - (1 - \tfrac{{2 - \lambda }}{p}),1 - \tfrac{{2 - \lambda }}{p})$$ \end{document} is the beta function. B *(λ) is proved to be best possible. A stronger form of this inequality is obtained by means of the Euler-Maclaurin summation formula.

scholarly journals Hermite–Hadamard-type inequalities for the interval-valued approximately h-convex functions via generalized fractional integrals

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Dafang Zhao ◽  
Muhammad Aamir Ali ◽  
Artion Kashuri ◽  
Hüseyin Budak ◽  
Mehmet Zeki Sarikaya
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Special Cases ◽  
Definition Of ◽  
The Given ◽  
Class Of Functions ◽  
Interval Valued ◽  
New Inequalities

Abstract In this paper, we present a new definition of interval-valued convex functions depending on the given function which is called “interval-valued approximately h-convex functions”. We establish some inequalities of Hermite–Hadamard type for a newly defined class of functions by using generalized fractional integrals. Our new inequalities are the extensions of previously obtained results like (D.F. Zhao et al. in J. Inequal. Appl. 2018(1):302, 2018 and H. Budak et al. in Proc. Am. Math. Soc., 2019). We also discussed some special cases from our main results.

scholarly journals On some inequalities in 2-metric spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mohamed Jleli ◽  
Bessem Samet
Keyword(s):  
Metric Spaces ◽  
New Inequalities

AbstractIn this paper, we establish new inequalities in the setting of 2-metric spaces and provide their geometric interpretations. Some of our results are extensions of those obtained by Dragomir and Goşa (J. Indones. Math. Soc. 11(1):33–38, 2005) in the setting of metric spaces.

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