Papers by Mohammad W. Alomari
Open Mathematics, Dec 31, 2022
This study systematically develops error estimates tailored to a specific set of general quadratu... more This study systematically develops error estimates tailored to a specific set of general quadrature rules that exclusively incorporate first derivatives. Moreover, it introduces refined versions of select generalized Ostrowski's type inequalities, enhancing their applicability. Through the skillful application of Hayashi's celebrated inequality to specific functions, the provided proofs underpin these advancements. Notably, this approach extends its utility to approximate integrals of real functions with bounded first derivatives. Remarkably, it employs Newton-Cotes and Gauss-Legendre quadrature rules, bypassing the need for stringent requirements on higher-order derivatives.
Axioms
This paper introduces several generalized extensions of some recent numerical radius inequalities... more This paper introduces several generalized extensions of some recent numerical radius inequalities of Hilbert space operators. More preciously, these inequalities refine the recent inequalities that were proved in literature. It has already been demonstrated that some inequalities can be improved or restored by concatenating some into one inequality. The main idea of this paper is to extend the existing numerical radius inequalities by providing a unified framework. We also present a numerical example to demonstrate the effectiveness of the proposed approach. Roughly, our approach combines the existing inequalities, proved in literature, into a single inequality that can be used to obtain improved or restored results. This unified approach allows us to extend the existing numerical radius inequalities and show their effectiveness through numerical experiments.
In this work, in spite of Milne’s recommendation using the three-point Newton–Cotes open formula ... more In this work, in spite of Milne’s recommendation using the three-point Newton–Cotes open formula (Milne’s rule) as a predictor rule and three-point Newton–Cotes closed formula (Simpson’s rule) as a corrector rule for 4-th differentiable functions with bounded derivatives. There is still a great need to introduce such formulas in other Lp spaces. Often, we need to approximate real integrals under the assumptions of the function involved. Because of that, the aim of this work is to introduce several Lp error estimates for the proposed perturbed Milne’s quadrature rule. Numerical experiments showing that our proposed quadrature rule is better than the classical Milne rule for certain types of functions are provided as well.
Symmetry
This paper proves several new inequalities for the Euclidean operator radius, which refine some r... more This paper proves several new inequalities for the Euclidean operator radius, which refine some recent results. It is shown that the new results are much more accurate than the related, recently published results. Moreover, inequalities for both symmetric and non-symmetric Hilbert space operators are studied.
In this work, new refinements of some numerical radius inequalities are proved. Namely, new impro... more In this work, new refinements of some numerical radius inequalities are proved. Namely, new improvements and refinements purify the recent inequalities of some famous inequalities concerning the numerical radius of Hilbert space operators. The proven inequalities in this work are not only an improvement over old inequalities, but rather they are stronger than them. Several examples that support the validity of our results are established as well.
arXiv (Cornell University), Sep 19, 2023
In this paper, we show several bounds for the numerical radius of a Hilbert space operator in ter... more In this paper, we show several bounds for the numerical radius of a Hilbert space operator in terms of the Euclidean operator norm. The obtained forms will enable us to find interesting refinements of celebrated results in the literature. Then, the f -operator radius, recently defined as a generalization of the Euclidean operator radius, will be studied. Many upper bounds will be found and matched with existing results that treat the numerical radius. Special cases of this discussion will lead to some refinements and generalizations of some well-established results in the field. Further, numerical examples are given to support our findings, and a simple optimization application will be presented.
Some companions of Ostrowski's integral inequality for the Riemann-Stieltjes integral b a f (t) d... more Some companions of Ostrowski's integral inequality for the Riemann-Stieltjes integral b a f (t) du (t), where f is assumed to be of r-H-Hölder type on [a, b] and u is of bounded variation on [a, b], are proved. Applications to the approximation problem of the Riemann-Stieltjes integral in terms of Riemann-Stieltjes sums are also pointed out.
Moroccan Journal of pure and applied analysis, Dec 1, 2016
In literature the Dragomir-Fedotov functional is well known as In this work a generalization of D... more In literature the Dragomir-Fedotov functional is well known as In this work a generalization of D (f ; u) is established. Namely, we define the weighted Dragomir-Fedotov functional such as: and hence several bounds are proved.
Journal of Mathematical Inequalities, 2023
In this work, the concept of the Davis-Wielandt Berezin number is introduced. Some upper and lowe... more In this work, the concept of the Davis-Wielandt Berezin number is introduced. Some upper and lower bounds for the Davis-Wielandt Berezin number are introduced. A connection between norm-parallelism to the identity operator and an equality condition for the Davis-Wielandt Berezin number are also discussed. Some bounds for the Davis-Wielandt Berezin number for n × n operator matrices are established.
arXiv (Cornell University), Mar 25, 2016
In literature the Hermite-Hadamard inequality was eligible for many reasons, one of the most surp... more In literature the Hermite-Hadamard inequality was eligible for many reasons, one of the most surprising and interesting that the Hermite-Hadamard inequality combine the midpoint and trapezoid formulae in an inequality. In this work, a Hermite-Hadamard like inequality that combines the composite trapezoid and composite midpoint formulae is proved. So that, the classical Hermite-Hadamard inequality becomes a special case of the presented result. Some Ostrowski's type inequalities for convex functions are proved as well.
arXiv (Cornell University), Dec 14, 2018
In this work, sharp Wirtinger type inequalities for double integrals are established. As applicat... more In this work, sharp Wirtinger type inequalities for double integrals are established. As applications, two sharp Čebyšev type inequalities for absolutely continuous functions whose second partial derivatives belong to L 2 space are proved.
In this paper, three point quadrature rules for the Riemann– Stieltjes integral are introduced. A... more In this paper, three point quadrature rules for the Riemann– Stieltjes integral are introduced. Applications to numerical integration are provided as well.
Filomat, 2023
In this paper, we generalize and refine some Berezin number inequalities for Hilbert space operat... more In this paper, we generalize and refine some Berezin number inequalities for Hilbert space operators. Namely, we refine the Hermite-Hadamard inequality and some other recent results by using the concept of superquadraticity and convexity. Then we extend these inequalities for the Berezin number. Among other inequalities, it is shown that if S, T ∈ L(H(Ω)) such that ber(T) ≤ ber(|S|) and f is a nonnegative superquadratic function, then f (ber (T)) ≤ ber( f (|S|)) -ℓ ber f (||S|ber (T)|) .
Annals of Functional Analysis, Aug 21, 2022
Advances in Pure and Applied Mathematics, Oct 1, 2019
In this work, operator version of Popoviciu's inequality for positive selfadjoint operators in Hi... more In this work, operator version of Popoviciu's inequality for positive selfadjoint operators in Hilbert spaces under positive linear maps for superquadratic functions is proved. Analogously, using the same technique operator version of Popoviciu's inequality for convex functions is obtained. Some other related inequalities are also deduced.
arXiv (Cornell University), Nov 1, 2022
In this paper, we introduce the f -operator radius of Hilbert space operators as a generalization... more In this paper, we introduce the f -operator radius of Hilbert space operators as a generalization of the Euclidean operator radius and the q-operator radius. Properties of the newly defined radius are discussed, emphasizing how it extends some known results in the literature.
Konuralp Journal of Mathematics (KJM), Oct 15, 2019
A weighted companion of Ostrowski-Midpoint type inequality is established. Application to a compo... more A weighted companion of Ostrowski-Midpoint type inequality is established. Application to a composite quadrature rule is provided.
Moroccan Journal of pure and applied analysis, Dec 1, 2018
In this work, we construct a new general two-point quadrature rules for the Riemann-Stieltjes int... more In this work, we construct a new general two-point quadrature rules for the Riemann-Stieltjes integral b a f (t) du (t), where the integrand f is assumed to be satisfied with the H ölder condition on [a, b] and the integrator u is of bounded variation on [a, b]. The dual formulas under the same assumption are proved. Some sharp error L p -Error estimates for the proposed quadrature rules are also obtained.
Constructive mathematical analysis, Sep 15, 2022
The Berezin transform A and the Berezin radius of an operator A on the reproducing kernel Hilbert... more The Berezin transform A and the Berezin radius of an operator A on the reproducing kernel Hilbert space over some set Q with normalized reproducing kernel kη := Kη Kη are defined, respectively, by A(η) = Akη, kη , η ∈ Q and ber(A) := sup η∈Q A(η) . A simple comparison of these properties produces the inequalities 1 4 In this research, we investigate other inequalities that are related to them. In particular, for A ∈ L (H (Q)) we prove that ber
Afrika Matematika, Apr 6, 2022
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Papers by Mohammad W. Alomari