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Search Results (4)

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Keywords = Dragomir extension

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22 pages, 286 KB  
Article
Ostrowski-Type Inequalities for Functions of Two Variables in Banach Spaces
by Muhammad Amer Latif and Ohud Bulayhan Almutairi
Mathematics 2024, 12(17), 2748; https://doi.org/10.3390/math12172748 - 4 Sep 2024
Cited by 1 | Viewed by 800
Abstract
In this paper, we offer Ostrowski-type inequalities that extend the findings that have been proven for functions of one variable with values in Banach spaces, conducted in a remarkable study by Dragomir, to functions of two variables containing values in the product Banach [...] Read more.
In this paper, we offer Ostrowski-type inequalities that extend the findings that have been proven for functions of one variable with values in Banach spaces, conducted in a remarkable study by Dragomir, to functions of two variables containing values in the product Banach spaces. Our findings are also an extension of several previous findings that have been established for functions of two variable functions. Prior studies on Ostrowski-type inequalities incriminated functions that have values in Banach spaces or Hilbert spaces. This study is unique and significant in the field of mathematical inequalities, and specifically in the study of Ostrowski-type inequalities, because they have been established for functions having values in a product of two Banach spaces. Full article
(This article belongs to the Special Issue Mathematical Analysis and Functional Analysis and Their Applications)
11 pages, 275 KB  
Article
Improvement of Furuta’s Inequality with Applications to Numerical Radius
by Mohammad W. Alomari, Mojtaba Bakherad, Monire Hajmohamadi, Christophe Chesneau, Víctor Leiva and Carlos Martin-Barreiro
Mathematics 2023, 11(1), 36; https://doi.org/10.3390/math11010036 - 22 Dec 2022
Cited by 4 | Viewed by 1769
Abstract
In diverse branches of mathematics, several inequalities have been studied and applied. In this article, we improve Furuta’s inequality. Subsequently, we apply this improvement to obtain new radius inequalities that not been reported in the current literature. Numerical examples illustrate the main findings. [...] Read more.
In diverse branches of mathematics, several inequalities have been studied and applied. In this article, we improve Furuta’s inequality. Subsequently, we apply this improvement to obtain new radius inequalities that not been reported in the current literature. Numerical examples illustrate the main findings. Full article
(This article belongs to the Special Issue Mathematical Inequalities, Models and Applications)
18 pages, 320 KB  
Article
On the Dragomir Extension of Furuta’s Inequality and Numerical Radius Inequalities
by Mohammad W. Alomari, Gabriel Bercu and Christophe Chesneau
Symmetry 2022, 14(7), 1432; https://doi.org/10.3390/sym14071432 - 12 Jul 2022
Cited by 3 | Viewed by 1802
Abstract
In this work, some numerical radius inequalities based on the recent Dragomir extension of Furuta’s inequality are obtained. Some particular cases are also provided. Among others, the celebrated Kittaneh inequality reads: wT≤12T+T*. It is [...] Read more.
In this work, some numerical radius inequalities based on the recent Dragomir extension of Furuta’s inequality are obtained. Some particular cases are also provided. Among others, the celebrated Kittaneh inequality reads: wT≤12T+T*. It is proved that wT≤12T+T*−12infx=1Tx,x12−T*x,x122, which improves on the Kittaneh inequality for symmetric and non-symmetric Hilbert space operators. Other related improvements to well-known inequalities in literature are also provided. Full article
(This article belongs to the Special Issue Inequality and Symmetry in Mathematical Analysis)
9 pages, 232 KB  
Article
On Some Inequalities Involving Liouville–Caputo Fractional Derivatives and Applications to Special Means of Real Numbers
by Bessem Samet and Hassen Aydi
Mathematics 2018, 6(10), 193; https://doi.org/10.3390/math6100193 - 8 Oct 2018
Cited by 16 | Viewed by 2746
Abstract
We are concerned with the class of functions f ∈ C 1 ( [ a , b ] ; R ) , a , b ∈ R , a < b , such that c D a α f is convex or [...] Read more.
We are concerned with the class of functions f ∈ C 1 ( [ a , b ] ; R ) , a , b ∈ R , a < b , such that c D a α f is convex or c D b α f is convex, where 0 < α < 1 , c D a α f is the left-side Liouville–Caputo fractional derivative of order α of f and c D b α f is the right-side Liouville–Caputo fractional derivative of order α of f. Some extensions of Dragomir–Agarwal inequality to this class of functions are obtained. A parallel development is made for the class of functions f ∈ C 1 ( [ a , b ] ; R ) such that c D a α f is concave or c D b α f is concave. Next, an application to special means of real numbers is provided. Full article
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