scholarly journals New Inequalities Similar to Hardy-Hilbert Inequality and their Applications

2007 ◽  
Vol 2007 (1) ◽  
pp. 090641
Author(s):  
Lü Zhongxue ◽  
Xie Hongzheng
Keyword(s):  
Hilbert Inequality ◽  
New Inequalities

Generalization of Hilbert Inequality with Some Parameters

2015 ◽  
Vol 65 (3) ◽  
Author(s):  
S. A. A. El-Marouf
Keyword(s):  
Hilbert Inequality ◽  
Special Cases ◽  
Weight Coefficients ◽  
New Inequalities

AbstractIn this paper, by introducing some parameters and estimating the weight coefficients, some new inequalities are established. All results of Hilbert, Hardy and Yang are considered as special cases of the new given inequalities.

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.

scholarly journals New dynamic Hilbert-type inequalities in two independent variables involving Fenchel–Legendre transform

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
A. A. El-Deeb ◽  
Saima Rashid ◽  
Zareen A. Khan ◽  
S. D. Makharesh
Keyword(s):  
Time Scales ◽  
Legendre Transform ◽  
Independent Variables ◽  
Hilbert Type ◽  
Two Independent Variables ◽  
New Inequalities

AbstractIn this paper, we establish some dynamic Hilbert-type inequalities in two independent variables on time scales by using the Fenchel–Legendre transform. We also apply our inequalities to discrete and continuous calculus to obtain some new inequalities as particular cases. Our results give more general forms of several previously established inequalities.

scholarly journals Post-quantum Hermite–Hadamard type inequalities for interval-valued convex functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Ghulam Murtaza ◽  
Yu-Ming Chu
Keyword(s):  
Convex Functions ◽  
Fundamental Properties ◽  
Interval Valued ◽  
New Inequalities

AbstractIn this research, we introduce the notions of $(p,q)$ ( p , q ) -derivative and integral for interval-valued functions and discuss their fundamental properties. After that, we prove some new inequalities of Hermite–Hadamard type for interval-valued convex functions employing the newly defined integral and derivative. Moreover, we find the estimates for the newly proved inequalities of Hermite–Hadamard type. It is also shown that the results proved in this study are the generalization of some already proved research in the field of Hermite–Hadamard inequalities.

Some Steffensen-type inequalities

2017 ◽  
Vol 8 (3) ◽  
Author(s):  
Mohammad W. Alomari ◽  
Sabir Hussain ◽  
Zheng Liu
Keyword(s):  
Integral Inequality ◽  
New Inequalities

AbstractIn this paper, new inequalities connected with the celebrated Steffensen’s integral inequality are proved.

On a Refinement of Hardy-Hilbert Inequality

2012 ◽  
Vol 166-169 ◽  
pp. 3027-3030
Author(s):  
Bao Ju Sun
Keyword(s):  
Weight Coefficient ◽  
Hilbert Inequality ◽  
Maximum Minimum

In this paper, by using Maximum-minimum monotonic theorem and estimating the weight coefficient, a refinement of Hardy- Hilbert inequality is established.

New inequalities for the Coulomb T matrix in momentum space

1984 ◽  
Vol 25 (10) ◽  
pp. 3033-3038 ◽  
Author(s):  
H. van Haeringen ◽  
L. P. Kok
Keyword(s):  
Momentum Space ◽  
T Matrix ◽  
New Inequalities

scholarly journals New Inequalities between Information Measures of Network Information Content

2013 ◽  
Vol 2013 ◽  
pp. 1-3 ◽  
Author(s):  
Pantelimon-George Popescu ◽  
Florin Pop ◽  
Alexandru Herişanu ◽  
Nicolae Ţăpuş
Keyword(s):  
Information Processing ◽  
Complex Systems ◽  
Complex Networks ◽  
Information Content ◽  
Discrete Case ◽  
Network Information ◽  
Information Inequalities ◽  
Information Measures ◽  
New Inequalities

We refine a classical logarithmic inequality using a discrete case of Bernoulli inequality, and then we refine furthermore two information inequalities between information measures for graphs, based on information functionals, presented by Dehmer and Mowshowitz in (2010) as Theorems 4.7 and 4.8. The inequalities refer to entropy-based measures of network information content and have a great impact for information processing in complex networks (a subarea of research in modeling of complex systems).

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