scholarly journals On Some Inequalities for the Generalized Euclidean Operator Radius

2019 ◽  
Author(s):  
Mohammad Alomari
Keyword(s):  
Numerical Radius ◽  
Interesting Generalization ◽  
New Inequalities

There are many criterion to generalize the concept of numerical radius; one of the most recent interesting generalization is what so-called the generalized Euclidean operator radius. Simply, it is the numerical radius of multivariable operators. In this work, several new inequalities, refinements, and generalizations are established for this kind of numerical radius.

scholarly journals Hilbert-Schmidt numerical radius of block operators

Filomat ◽  
2021 ◽  
Vol 35 (8) ◽  
pp. 2663-2678
Author(s):  
Satyajit Sahoo ◽  
Mohammad Sababheh
Keyword(s):  
Numerical Radius ◽  
New Inequalities

The main goal of this article is to present new inequalities for the recently defined generalized numerical radius of block operators.

scholarly journals Some Improvements of the Cauchy-Schwarz Inequality Using the Tapia Semi-Inner-Product

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2112
Author(s):  
Nicuşor Minculete ◽  
Hamid Reza Moradi
Keyword(s):  
Hilbert Space ◽  
Normed Space ◽  
Triangle Inequality ◽  
Schwarz Inequality ◽  
Inner Product ◽  
Numerical Radius ◽  
Real Numbers ◽  
Norm Inequalities ◽  
Hilbert Space Operators ◽  
New Inequalities

The aim of this article is to establish several estimates of the triangle inequality in a normed space over the field of real numbers. We obtain some improvements of the Cauchy–Schwarz inequality, which is improved by using the Tapia semi-inner-product. Finally, we obtain some new inequalities for the numerical radius and norm inequalities for Hilbert space operators.

IMPROVED INEQUALITIES FOR THE NUMERICAL RADIUS: WHEN INVERSE COMMUTES WITH THE NORM

2018 ◽  
Vol 97 (2) ◽  
pp. 293-296 ◽  
Author(s):  
BRYAN E. CAIN
Keyword(s):  
Hilbert Space ◽  
Numerical Radius ◽  
Bounded Linear ◽  
Hilbert Space Operators ◽  
New Inequalities

New inequalities relating the norm $n(X)$ and the numerical radius $w(X)$ of invertible bounded linear Hilbert space operators were announced by Hosseini and Omidvar [‘Some inequalities for the numerical radius for Hilbert space operators’, Bull. Aust. Math. Soc.94 (2016), 489–496]. For example, they asserted that $w(AB)\leq$$2w(A)w(B)$ for invertible bounded linear Hilbert space operators $A$ and $B$. We identify implicit hypotheses used in their discovery. The inequalities and their proofs can be made good by adding the extra hypotheses which take the form $n(X^{-1})=n(X)^{-1}$. We give counterexamples in the absence of such additional hypotheses. Finally, we show that these hypotheses yield even stronger conclusions, for example, $w(AB)=w(A)w(B)$.

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.

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