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 He has the same number of unpublished preprints and drafts.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
Scopus Publications
Scholar Citations
Scholar h-index
Scholar i10-index
Scopus Publications
, 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.
Mohammad W. Alomari, Iqbal M. Batiha, Abeer Al-Nana, Mohammad Odeh, Nidal Anakira, and Shaher Momani
Universitas Muhammadiyah Yogyakarta
This study introduces a novel higher-order implicit correction method derived from the Euler-Maclaurin formula to enhance the approximation of initial value problems. The proposed method surpasses the Runge-Kutta approach in accuracy, stability, and convergence. An error bound is established to demonstrate its theoretical reliability. To validate its effectiveness, numerical experiments are conducted, showcasing its superior performance compared to conventional methods. The results consistently confirm that the proposed method outperforms the Runge-Kutta method across various practical applications.
Mohammad W. Alomari, Iqbal M. Batiha, Nidal Anakira, Ala Amourah, Iqbal H. Jebril, and Shaher Momani
Universitas Muhammadiyah Yogyakarta
This work is dedicated to advancing the approximation of initial value problems through the introduction of an innovative and superior method inspired by Taylor’s approach. Specifically, we present an enhanced variant achieved by accelerating the expansion of the Obreschkoff formula. This results in a higher-order implicit corrected method that outperforms Rung– Kutta’s (RK) method in terms of accuracy. We derive an error bound for the Obreschkoff higher-order method, showcasing its stability, convergence, and greater efficiency than the conventional RK method. To substantiate our claims, numerical experiments are provided, highlighting the exceptional efficacy of our proposed method over the traditional RK method.
Mohammad W. Alomari
Springer Science and Business Media LLC
Mohammad W. Alomari, Iqbal M. Batiha, and Shaher Momani
Springer Science and Business Media LLC
Mohammad W. Alomari, Mojtaba Bakherad, and Monire Hajmohamadi
Springer Science and Business Media LLC
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 ].
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.
Abeer A. Al-Nana, Mohammed W. Alomari, and Iqbal M. Batiha
Praise Worthy Prize
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.
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.
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.
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.
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.
Mohammad W. Alomari, Nazia Irshad, Asif R. Khan, and Muhammad Awais Shaikh
Element d.o.o.
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.
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.
Mohammad W. Alomari, Monire Hajmohamadi, and Mojtaba Bakherad
Element d.o.o.
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.