Mohammad W. Alomari
@jadara.edu.jo
Department of Mathematics
Jadara University
Prof. Alomari is a Full Professor of Mathematics (Real Analysis-Inequalities) at Jadara University-Jordan. His main research area includes; Analytic inequalities, Approximation theory, Hilbert space, and Theory of real functions. Since 2008, Prof. Alomari published more than 100 articles in his research area. He has the same number of unpublished preprints and drafts.
RESEARCH, TEACHING, or OTHER INTERESTS
Analysis, General Mathematics, Numerical Analysis, Mathematics
72
Scopus Publications
3598
Scholar Citations
28
Scholar h-index
54
Scholar i10-index
Scopus Publications
- Numerical Advancements: A Duel between Euler-Maclaurin and Runge-Kutta for Initial Value Problem
, Iqbal Iqbal, , , , , , Mohammad W. Alomari, Nidal Anakira, Saad Meqdad,et al.
American Scientific Publishing Group (ASPG) LLC
This work is dedicated to advancing the approximation of initial value problems through the introduction of an innovative and superior method inspired by the Euler-Maclaurin formula. This results in a higher-order implicit corrected method that outperforms the Runge-Kutta method in terms of accuracy. We derive an error bound for the Euler-Maclaurin higher-order method, showcasing its stability, convergence, and greater efficiency compared to the conventional Runge-Kutta method. To substantiate our claims, numerical experiments are provided, highlighting the exceptional efficiency of our proposed method over the traditional well-known methods. In conclusion, the proposed method consistently outperforms the Runge-Kutta method experimentally in all practical problems. - 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.
RECENT SCHOLAR PUBLICATIONS
- 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 - GRSS TYPE INEQUALITIES OVER p-DISKS WITH APPLICATIONS
MW Alomari
Journal of Mathematical Sciences, 1-16 2025 - Revolutionizing Numerical Approximations: A Novel Higher-Order Implicit Method vs. Runge-Kutta for Initial Value Problems
MW Alomari, IM Batiha, N Anakira, A Amourah, IH Jebril, S Momani
Journal of Robotics and Control (JRC) 6 (2), 624-637 2025 - 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 25 (3), 76-91 2025 - New Higher-Order Implicit Method for Approximating Solutions of Boundary-Value Problems
SM Iqbal M Batiha, Mohammad W Alomari, Iqbal H Jebril, Thabet Abdeljawad ...
International Journal of Neutrosophic Science 25 (4), 389-398 2025 - Euler-Maclaurin Method for Approximating Solutions of Initial Value Problems.
MW Alomari, IM Batiha, WA Alkasasbeh, N Anakira, IH Jebril, S Momani
International Journal of Robotics & Control Systems 5 (1) 2025 - 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 70 (4), 3369-3393 2024 - 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 - The Modified Taylor Method for Approximating Solutions of Initial Value Problems
AA Al-Nana, MW Alomari, IM Batiha
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
MOST CITED SCHOLAR PUBLICATIONS
- 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: 329 - 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: 258 - 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: 207 - 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: 198 - 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: 188 - 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: 170 - 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: 154 - 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: 147 - 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: 133 - 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: 132 - Hadamard-type inequalities for s-convex functions
M Alomari, M Darus
Int. Math. Forum 3 (40), 1965-1975 2008
Citations: 99 - 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: 94 - Integral inequalities via several kinds of convexity
ME zdemir, E Set, M Alomari
Creat. Math. Inform 20 (1), 62-73 2011
Citations: 91 - 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: 66 - 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: 65 - Two inequalities of Simpson type for quasi-convex functions and applications
M Alomari, S Hussain
Appl. Math. E-Notes 11, 110-117 2011
Citations: 58 - A companion of Ostrowski’s inequality with applications
MW Alomari
Transylv. J. Math. Mech 3 (1), 9-14 2011
Citations: 49 - 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 for mappings whose first derivatives are bounded and applications in numerical integration
MW Alomari
Kragujevac Journal of Mathematics 36 (38), 77-82 2012
Citations: 46 - 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: 42