@jadara.edu.jo

Department of Mathematics

Jadara University

Analysis, General Mathematics, Numerical Analysis, Mathematics

69

Scopus Publications

3379

Scholar Citations

27

Scholar h-index

51

Scholar i10-index

- New higher-order implict method for approximating solutions of the initial value problems

Mohammad W. Alomari, Iqbal M. Batiha, and Shaher Momani

Springer Science and Business Media LLC - A generalization of the Davis–Wielandt radius for operators

Mohammad W. Alomari, Mojtaba Bakherad, and Monire Hajmohamadi

Springer Science and Business Media LLC - On Cauchy–Schwarz type inequalities and applications to numerical radius inequalities

M. Alomari

In this work, a refinement of the Cauchy–Schwarz inequality in inner product space is proved. A more general refinement of the Kato’s inequality or the so called mixed Schwarz inequality is established. Refinements of some famous numerical radius inequalities are also pointed out. As shown in this work, these refinements generalize and refine some recent and old results obtained in literature. Among others, it is proved that if $$T\\in \\mathscr {B}\\left( \\mathscr {H}\\right) $$ T ∈ B H , then $$\\begin{aligned} \\omega ^{2}\\left( T\\right)&\\le \\frac{1}{12} \\left\\| \\left| T \\right| +\\left| {T^* } \\right| \\right\\| ^2 + \\frac{1}{3} \\omega \\left( T\\right) \\left\\| \\left| T \\right| +\\left| {T^* } \\right| \\right\\| \\\\&\\le \\frac{1}{6} \\left\\| \\left| T \\right| ^2+ \\left| {T^* } \\right| ^2 \\right\\| + \\frac{1}{3} \\omega \\left( T\\right) \\left\\| \\left| T \\right| +\\left| {T^* } \\right| \\right\\| , \\end{aligned}$$ ω 2 T ≤ 1 12 T + T ∗ 2 + 1 3 ω T T + T ∗ ≤ 1 6 T 2 + T ∗ 2 + 1 3 ω T T + T ∗ , which refines the recent inequality obtained by Kittaneh and Moradi in [ 10 ]. - Generalized Euclidean operator radius

Mohammad W. Alomari, Mohammad Sababheh, Cristian Conde, and Hamid Reza Moradi

Walter de Gruyter GmbH

Abstract 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. The properties of the newly defined radius are discussed, emphasizing how it extends some known results in the literature. - On Further Refinements of Numerical Radius Inequalities

Ayman Hazaymeh, Ahmad Qazza, Raed Hatamleh, Mohammad W. Alomari, and Rania Saadeh

MDPI AG

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. - A Perturbed Milne’s Quadrature Rule for n-Times Differentiable Functions with L<sup>p</sup>-Error Estimates

Ayman Hazaymeh, Rania Saadeh, Raed Hatamleh, Mohammad W. Alomari, and Ahmad Qazza

MDPI AG

In this work, a perturbed Milne’s quadrature rule for n-times differentiable functions with Lp-error estimates is derived. One of the most important advantages of our result is that it is verified for p-variation and Lipschitz functions. Several error estimates involving Lp-bounds are proven. These estimates are useful if the fourth derivative is unbounded in L∞-norm or the Lp-error estimate is less than the L∞-error estimate. Furthermore, since the classical Milne’s quadrature rule cannot be applied either when the fourth derivative is unbounded or does not exist, the proposed quadrature could be used alternatively. Numerical experiments showing that our proposed quadrature rule is better than the classical Milne rule for certain types of functions are also provided. The numerical experiments compare the accuracy of the proposed quadrature rule to the classical Milne rule when approximating different types of functions. The results show that, for certain types of functions, the proposed quadrature rule is more accurate than the classical Milne rule. - Further Accurate Numerical Radius Inequalities

Tariq Qawasmeh, Ahmad Qazza, Raed Hatamleh, Mohammad W. Alomari, and Rania Saadeh

MDPI AG

The goal of this study is to refine some numerical radius inequalities in a novel way. The new improvements and refinements purify some famous inequalities pertaining to Hilbert space operators numerical radii. The inequalities that have been demonstrated in this work are not only an improvement over old inequalities but also stronger than them. Several examples supporting the validity of our results are provided as well. - On Some Inequalities for the Generalized Euclidean Operator Radius

Mohammad W. Alomari, Gabriel Bercu, Christophe Chesneau, and Hala Alaqad

MDPI AG

In the literature, there are many criteria to generalize the concept of a numerical radius; one of the most recent and interesting generalizations is the so-called generalized Euclidean operator radius, which reads: ωpT1,⋯,Tn:=supx=1∑i=1nTix,xp1/p,p≥1, for all Hilbert space operators T1,⋯,Tn. Simply put, it is the numerical radius of multivariable operators. This study establishes a number of new inequalities, extensions, and generalizations for this type of numerical radius. More precisely, by utilizing the mixed Schwarz inequality and the extension of Furuta’s inequality, some new refinement inequalities are obtained for the numerical radius of multivariable Hilbert space operators. In the case of n=1, the resulting inequalities could be considered extensions and generalizations of the classical numerical radius. - Refinements of the Euclidean Operator Radius and Davis–Wielandt Radius-Type Inequalities

Tareq Hamadneh, Mohammad W. Alomari, Isra Al-Shbeil, Hala Alaqad, Raed Hatamleh, Ahmed Salem Heilat, and Abdallah Al-Husban

MDPI AG

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. - GENERALIZATION OF TWO-POINT OSTROWSKI’S INEQUALITY

Mohammad W. Alomari, Nazia Irshad, Asif R. Khan, and Muhammad Awais Shaikh

Element d.o.o. - An application of Hayashi's inequality in numerical integration

Ahmed Salem Heilat, Ahmad Qazza, Raed Hatamleh, Rania Saadeh, and Mohammad W. Alomari

Walter de Gruyter GmbH

Abstract 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. - A Solution of the Complex Fuzzy Heat Equation in Terms of Complex Dirichlet Conditions Using a Modified Crank-Nicolson Method

Hamzeh Zureigat, Mohammad A. Tashtoush, Ali F. Al Jassar, Emad A. Az-Zo’bi, and Mohammad W. Alomari

Hindawi Limited

Complex fuzzy sets (CFSs) have recently emerged as a potent tool for expanding the scope of fuzzy sets to encompass wider ranges within the unit disk in the complex plane. This study explores complex fuzzy numbers and introduces their application for the first time in the literature to address a complex fuzzy partial differential equation that involves a complex fuzzy heat equation under Hukuhara differentiability. The researchers utilize an implicit finite difference scheme, namely the Crank–Nicolson method, to tackle complex fuzzy heat equations. The problem’s fuzziness arises from the coefficients in both amplitude and phase terms, as well as in the initial and boundary conditions, with the Convex normalized triangular fuzzy numbers extended to the unit disk in the complex plane. The researchers take advantage of the properties and benefits of CFS theory in the proposed numerical methods and subsequently provide a new proof of the stability under CFS theory. A numerical example is presented to demonstrate the proposed approach’s reliability and feasibility, with the results showing good agreement with the exact solution and relevant theoretical aspects. - NORM–PARALLELISM OF HILBERT SPACE OPERATORS AND THE DAVIS–WIELANDT BEREZIN NUMBER

Mohammad W. Alomari, Monire Hajmohamadi, and Mojtaba Bakherad

Element d.o.o. - Improvement of Furuta’s Inequality with Applications to Numerical Radius

Mohammad W. Alomari, Mojtaba Bakherad, Monire Hajmohamadi, Christophe Chesneau, Víctor Leiva, and Carlos Martin-Barreiro

MDPI AG

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. - On the Davis–Wielandt radius inequalities of Hilbert space operators

M. W. Alomari

Informa UK Limited

In this work, some new upper and lower bounds of the Davis-Wielandt radius are introduced. Generalizations of some presented results are obtained. Some bounds of the Davis-Wielandt radius for $n\\times n$ operator matrices are established. An extension of the Davis-Wielandt radius to the Euclidean operator radius is introduced. - Operator Jensen’s Inequality for Operator Superquadratic Functions

Mohammad W. Alomari, Christophe Chesneau, and Ahmad Al-Khasawneh

MDPI AG

In this work, an operator superquadratic function (in the operator sense) for positive Hilbert space operators is defined. Several examples with some important properties together with some observations which are related to the operator convexity are pointed out. A general Bohr’s inequality for positive operators is thus deduced. A Jensen-type inequality is proved. Equivalent statements of a non-commutative version of Jensen’s inequality for operator superquadratic function are also established. Finally, several trace inequalities for superquadratic functions (in the ordinary sense) are provided as well. - Improvements of trace inequalities for convex functions

Mohsen Kian and Mohammad W. Alomari

Springer Science and Business Media LLC - On the Dragomir Extension of Furuta’s Inequality and Numerical Radius Inequalities

Mohammad W. Alomari, Gabriel Bercu, and Christophe Chesneau

MDPI AG

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. - Improvement of Some Hayashi–Ostrowski Type Inequalities with Applications in a Probability Setting

Mohammad W. Alomari, Christophe Chesneau, Víctor Leiva, and Carlos Martin-Barreiro

MDPI AG

Different types of mathematical inequalities have been largely analyzed and employed. In this paper, we introduce improvements to some Ostrowski type inequalities and present their corresponding proofs. The presented proofs are based on applying the celebrated Hayashi inequality to certain functions. We provide examples that show these improvements. Illustrations of the obtained results are stated in a probability framework. - Some Generalized Euclidean Operator Radius Inequalities

Mohammad W. Alomari, Khalid Shebrawi, and Christophe Chesneau

MDPI AG

In this work, some generalized Euclidean operator radius inequalities are established. Refinements of some well-known results are provided. Among others, some bounds in terms of the Cartesian decomposition of a given Hilbert space operator are proven. - Bounding the Zeros of Polynomials Using the Frobenius Companion Matrix Partitioned by the Cartesian Decomposition

Mohammad W. Alomari and Christophe Chesneau

MDPI AG

In this work, some new inequalities for the numerical radius of block n-by-n matrices are presented. As an application, the bounding of zeros of polynomials using the Frobenius companion matrix partitioned by the Cartesian decomposition method is proved. We highlight several numerical examples showing that our approach to bounding zeros of polynomials could be very effective in comparison with the most famous results as well as some recent results presented in the field. Finally, observations, a discussion, and a conclusion regarding our proposed bound of zeros are considered. Namely, it is proved that our proposed bound is more efficient than any other bound under some conditions; this is supported with many polynomial examples explaining our choice of restrictions. - On h-superquadratic functions

Mohammad W. Alomari and Christophe Chesneau

Springer Science and Business Media LLC - Grüss-Type Inequalities for Vector-Valued Functions

Mohammad W. Alomari, Christophe Chesneau, and Víctor Leiva

MDPI AG

Grüss-type inequalities have been widely studied and applied in different contexts. In this work, we provide and prove vectorial versions of Grüss-type inequalities involving vector-valued functions defined on Rn for inner- and cross-products.

- Generalisation of Companion of Ostrowski’s Type Inequality Via Riemann-Liouville Fractional Integral for Mappings whose 1st Derivatives are Bounded with Applications

F MEHMOOD, AR KHAN, MA SHAIKH, MW ALOMARI

Kragujevac Journal of Mathematics 50 (2), 273-286 2026 - Numerical Advancements: A Duel between Euler-Maclaurin and Runge-Kutta for Initial Value Problem

IM Batiha, MW Alomari, N Anakira, S Meqdad, IH Jebril, S Momani

International Journal of Neutrosophic Science, 76-6-91 2025 - Differential q-calculus of Several Variables

MW Alomari, WG Alshanti, I Batiha, L Guran, IH Jebril

Results in Nonlinear Analysis 7 (3), 109–129-109–129 2024 - A generalization of the Davis–Wielandt radius for operators

MW Alomari, M Bakherad, M Hajmohamadi

Boletn de la Sociedad Matemtica Mexicana 30 (2), 57 2024 - On Cauchy–Schwarz type inequalities and applications to numerical radius inequalities

MW Alomari

Ricerche di Matematica 73 (3), 1493-1510 2024 - Generalized Euclidean operator radius

MW Alomari, M Sababheh, C Conde, HR Moradi

Georgian Mathematical Journal 31 (3), 369-380 2024 - New higher-order implict method for approximating solutions of the initial value problems

MW Alomari, IM Batiha, S Momani

Journal of Applied Mathematics and Computing, 1-25 2024 - An application of Hayashi's inequality in numerical integration

AS Heilat, A Qazza, R Hatamleh, R Saadeh, MW Alomari

Open Mathematics 21 (1), 20230162 2023 - GENERALIZATION OF TWO–POINT OSTROWSKI’S INEQUALITY

MW Alomari, N Irshad, AR Khan, MA Shaikh

Journal of Mathematical Inequalities 17 (4), 1481-1509 2023 - On further refinements of numerical radius inequalities

A Hazaymeh, A Qazza, R Hatamleh, MW Alomari, R Saadeh

Axioms 12 (9), 807 2023 - A Perturbed Milne’s Quadrature Rule for n-Times Differentiable Functions with Lp-Error Estimates

A Hazaymeh, R Saadeh, R Hatamleh, MW Alomari, A Qazza

ِAxioms 12 (9), 803 2023 - Further accurate numerical radius inequalities

T Qawasmeh, A Qazza, R Hatamleh, MW Alomari, R Saadeh

Axioms 12 (8), 801 2023 - On the Davis–Wielandt radius inequalities of Hilbert space operators

MW Alomari

Linear and Multilinear Algebra 71 (11), 1804-1828 2023 - Refinements of the Euclidean operator radius and Davis–Wielandt radius-type inequalities

T Hamadneh, MW Alomari, I Al-Shbeil, H Alaqad, R Hatamleh, AS Heilat, ...

Symmetry 15 (5), 1061 2023 - Norm–Parallelism of Hilbert Space Operators and the Davis–Wielandt Berezin Number

MW ALOMARI, M Hajmohamadi, M Bakherad

Journal of Mathematical Inequalities 17 (1), 231–258 2023 - A solution of the complex fuzzy heat equation in terms of complex dirichlet conditions using a modified crank–nicolson method

H Zureigat, MA Tashtoush, AFA Jassar, EA Az-Zo’bi, MW Alomari

Advances in Mathematical Physics 2023 (1), 6505227 2023 - Refined Berezin number inequalities via superquadratic and convex functions

F Chien, M Bakherad, MW Alomari

Filomat 37 (1), 265-277 2023 - Improvement of Furuta’s Inequality with Applications to Numerical Radius

MW Alomari, M Bakherad, M Hajmohamadi, C Chesneau, V Leiva, ...

Mathematics 11 (1), 36 2022 - Operator Jensen’s inequality for operator superquadratic functions

MW Alomari, C Chesneau, A Al-Khasawneh

Axioms 11 (11), 617 2022 - Improvements of trace inequalities for convex functions

M Kian, MW Alomari

Annals of Functional Analysis 13 (4), 64 2022

- Ostrowski type inequalities for functions whose derivatives are s-convex in the second sense

M Alomari, M Darus, SS Dragomir, P Cerone

Applied mathematics letters 23 (9), 1071-1076 2010

Citations: 324 - New inequalities of Simpson's type for s-convex functions with applications

M Alomari, M Darus, SS Dragomir

Research report collection 12 (4) 2009

Citations: 245 - Refinements of Hadamard-type inequalities for quasi-convex functions with applications to trapezoidal formula and to special means

M Alomari, M Darus, US Kirmaci

Computers & mathematics with applications 59 (1), 225-232 2010

Citations: 196 - The Hadamard’s inequality for s-convex function of 2-variables on the co-ordinates

M Alomari, M Darus

Int. J. Math. Anal 2 (13), 629-638 2008

Citations: 196 - Inequalities of Hermite-Hadamard's type for functions whose derivatives absolute values are quasi-convex

M Alomari, M Darus, SS Dragomir

Research report collection 12 (Supp) 2009

Citations: 184 - On the Hadamard's inequality for log-convex functions on the coordinates

M Alomari, M Darus

Journal of Inequalities and Applications 2009, 1-13 2009

Citations: 157 - Some inequalities of Hermite-Hadamard type for s-convex functions

MW Alomari, M Darus, US Kirmaci

Acta Mathematica Scientia 31 (4), 1643-1652 2011

Citations: 152 - Hadamard-type inequalities for product two convex functions on the co-ordinates

MA Latif, M Alomari

International Mathematical Forum 4 (47), 2327-2338 2009

Citations: 141 - Some Ostrowski type inequalities for quasi-convex functions with applications to special means

M Alomari, M Darus

RGMIA Res. Rep. Coll 13 (2), 6 2010

Citations: 133 - On Hadamard-type inequalities for h-convex functions on the co-ordinates

MA Latif, M Alomari

Int. J. Math. Anal 3 (33), 1645-1656 2009

Citations: 127 - Hadamard-type inequalities for s-convex functions

M Alomari, M Darus

Int. Math. Forum 3 (40), 1965-1975 2008

Citations: 100 - Integral inequalities via several kinds of convexity

ME zdemir, E Set, M Alomari

Creat. Math. Inform 20 (1), 62-73 2011

Citations: 89 - Co-ordinated s-convex function in the first sense with some Hadamard-type inequalities

M Alomari, M Darus

Int. J. Contemp. Math. Sci 3 (32), 1557-1567 2008

Citations: 88 - On some inequalities of Simpson-type via quasi-convex functions and applications

M Alomari, M Darus

Transylvanian Journal of Mathematics and Mechanics 2 (1), 15-24 2010

Citations: 63 - A companion of Dragomir's generalization of Ostrowski's inequality and applications in numerical integration

MW Alomari

Ukrains’ kyi Matematychnyi Zhurnal 64 (4), 435-450 2012

Citations: 59 - Two inequalities of Simpson type for quasi-convex functions and applications

M Alomari, S Hussain

Appl. Math. E-Notes 11, 110-117 2011

Citations: 55 - Generalized double-integral Ostrowski type inequalities on time scales

S Hussain, MA Latif, M Alomari

Applied Mathematics Letters 24 (8), 1461-1467 2011

Citations: 48 - A companion of Ostrowski’s inequality with applications

MW Alomari

Transylv. J. Math. Mech 3 (1), 9-14 2011

Citations: 48 - A companion of Ostrowski's inequality for mappings whose first derivatives are bounded and applications in numerical integration

MW Alomari

Kragujevac Journal of Mathematics 36 (38), 77-82 2012

Citations: 45 - A generalization of weighted companion of Ostrowski integral inequality for mappings of bounded variation

MW Alomari

International Journal of Nonlinear Sciences and Numerical Simulation 21 (7-8 2020

Citations: 41