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 He has the same number of unpublished preprints and drafts.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
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Scopus Publications
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.
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.
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.
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.
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.
Mohsen Kian and Mohammad W. Alomari
Springer Science and Business Media LLC
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.
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.
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.
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.
Mohammad W. Alomari and Christophe Chesneau
Springer Science and Business Media LLC
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.
Mohammad W. Alomari and Milica Klaričić Bakula
MDPI AG
In this work, we offer new applications of Hayashi’s inequality for differentiable functions by proving new error estimates of the Ostrowski- and trapezoid-type quadrature rules.
Dulfikar Jawad Hashim, N. R. Anakira, Ali Fareed Jameel, A. K. Alomari, Hamzeh Zureigat, M. W. Alomari, and Teh Yuan Ying
Hindawi Limited
In this work, the fuzzy fractional two-point boundary value problems (FFTBVPs) are analyzed and solved using the fuzzy fractional homotopy analysis method (FF-HAM). Fuzzy set theory mixed with Caputo fractional derivative properties is utilized to produce a new formulation of the standard HAM in the fuzzy domain for the persistence of approximation series solutions for fuzzy fractional differential equations with boundary conditions. The FF-HAM provides a suitable way of controlling the convergence of the series solution through the advantage of the convergence control parameter, which plays a pivotal role in solving a wide range of mathematical problems. The convergence analysis algorithm has been described, along with a graphical representation of the FF-HAM of the proposed applications. The method produces high accuracy solutions with simple implementation for solving linear and nonlinear fuzzy fractional boundary value problems associated with physical application. Also, the obtained results are analyzed and compared with those present in the literature to show the efficiency of the FF-HAM.
Mehmet GÜRDAL and Mohammad ALOMARI
Constructive Mathematical Analysis
The Berezin transform $\\widetilde{A}$ and the Berezin radius of an operator $A$ on the reproducing kernel Hilbert space over some set $Q$ with normalized reproducing kernel $k_{\\eta}:=\\dfrac{K_{\\eta}}{\\left\\Vert K_{\\eta}\\right\\Vert}$ are defined, respectively, by $\\widetilde{A}(\\eta)=\\left\\langle {A}k_{\\eta},k_{\\eta}\\right\\rangle$, $\\eta\\in Q$ and $\\mathrm{ber} (A):=\\sup_{\\eta\\in Q}\\left\\vert \\widetilde{A}{(\\eta)}\\right\\vert$. A simple comparison of these properties produces the inequalities $\\dfrac{1}{4}\\left\\Vert A^{\\ast}A+AA^{\\ast}\\right\\Vert \\leq\\mathrm{ber}^{2}\\left( A\\right) \\leq\\dfrac{1}{2}\\left\\Vert A^{\\ast}A+AA^{\\ast}\\right\\Vert $. In this research, we investigate other inequalities that are related to them. In particular, for $A\\in\\mathcal{L}\\left( \\mathcal{H}\\left(Q\\right) \\right) $ we prove that$\\mathrm{ber}^{2}\\left( A\\right) \\leq\\dfrac{1}{2}\\left\\Vert A^{\\ast}A+AA^{\\ast}\\right\\Vert _{\\mathrm{ber}}-\\dfrac{1}{4}\\inf_{\\eta\\in Q}\\left(\\left( \\widetilde{\\left\\vert A\\right\\vert }\\left( \\eta\\right)\\right)-\\left( \\widetilde{\\left\\vert A^{\\ast}\\right\\vert }\\left( \\eta\\right)\\right) \\right) ^{2}.$
Ala Amourah, Mohammad Alomari, Feras Yousef, and Abdullah Alsoboh
Hindawi Limited
In this work, we introduce and investigate a new subclass of analytic bi-univalent functions based on subordination conditions between the zero-truncated Poisson distribution and Gegenbauer polynomials. More precisely, we will estimate the first two initial Taylor–Maclaurin coefficients and solve the Fekete–Szegö functional problem for functions belonging to this new subclass.