# Mohammad W. Alomari

Verified email at gmail.com

Department of Mathematics
Irbid National University

## RESEARCH INTERESTS

Inequalities, Expansions and Approximations

34

Scopus Publications

2121

24

36

## Scopus Publications

• Bounds for the difference between two Čebyšev functionals

Afrika Matematika, ISSN: 10129405, eISSN: 21907668, Issue: 3-4, Pages: 539-556, Published: 1 June 2020 Springer Science and Business Media LLC
In this work, a generalization of pre-Gruss inequality is established. Several bounds for the difference between two Cebysev functional are proved.

• Sharp wirtinger’s type inequalities for double integrals with applications

Novi Sad Journal of Mathematics, ISSN: 14505444, eISSN: 24062014, Pages: 1-16, Published: 2020 Faculty of Sciences, University of Novi Sad
In this work, sharp Wirtinger type inequalities for double integrals are established. As applications, two sharp \v{C}eby\v{s}ev type inequalities for absolutely continuous functions whose second partial derivatives belong to $L^2$ space are proved.

• A generalization of weighted companion of Ostrowski integral inequality for mappings of bounded variation

International Journal of Nonlinear Sciences and Numerical Simulation, ISSN: 15651339, Published: 2020 Walter de Gruyter GmbH
AbstractA weighted companion of Ostrowski type inequality is established. Some sharp inequalities are proved. Application to a quadrature rule is provided.

• On the generalized mixed Schwarz inequality

Proceedings of the Institute of Mathematics and Mechanics, ISSN: 24094986, eISSN: 24094994, Pages: 3-15, Published: 2020 ASOS Yayinevi
In this work, an extension of the generalized mixed Schwarz inequality is proved. A companion of the generalized mixed Schwarz inequality is established by merging both Cartesian and Polar decompositions of operators. Based on that some numerical radius inequalities are proved.

• Some properties of h-MN-convexity and Jensen’s type inequalities

Journal of Interdisciplinary Mathematics, ISSN: 09720502, Pages: 1349-1395, Published: 17 November 2019 Informa UK Limited

• Operator Popoviciu's inequality for superquadratic and convex functions of selfadjoint operators in Hilbert spaces

Advances in Pure and Applied Mathematics, ISSN: 18671152, eISSN: 18696090, Pages: 313-324, Published: 1 October 2019 Walter de Gruyter GmbH
Abstract In this work, an operator version of Popoviciu’s inequality for positive operators on Hilbert spaces under positive linear maps for superquadratic functions is proved. Analogously, using the same technique, an operator version of Popoviciu’s inequality for convex functions is obtained. Some other related inequalities are also presented.

• On Pompeiu–Chebyshev Functional and Its Generalization

Results in Mathematics, ISSN: 14226383, eISSN: 14209012, Published: 1 March 2019 Springer Science and Business Media LLC
In this work, a generalization of Chebyshev functional is presented. New inequalities of Grüss type via Pompeiu’s mean value theorem are established. Improvements of some old inequalities are proved. A generalization of pre-Grüss inequality is elaborated. Some remarks to further generalization of Chebyshev functional are presented. As applications, bounds for the reverse of CBS inequality are deduced. Hardy type inequalities on bounded real interval $$\left[ a,b\right]$$a,b under some other circumstances are introduced. Other related ramified inequalities for differentiable functions are also given.

• Refinements of some numerical radius inequalities for Hilbert space operators

Linear and Multilinear Algebra, ISSN: 03081087, eISSN: 15635139, Published: 2019 Informa UK Limited
In this work, some generalizations and refinements inequalities for numerical radius of the product of Hilbert space operators are proved. New inequalities for numerical radius of block matrices of Hilbert space operators are also established.

• Pompeiu-Čebyšev type inequalities for selfadjoint operators in Hilbert spaces

Advances in Operator Theory, eISSN: 2538225X, Pages: 459-472, Published: 1 June 2018 Tusi Mathematical Research Group
In this work, generalization of some inequalities for continuous $h$-synchronous ($h$-asynchronous) functions of selfadjoint linear operators in Hilbert spaces are proved.

• Two-Point Ostrowski’s Inequality

Results in Mathematics, ISSN: 14226383, eISSN: 14209012, Pages: 1499-1523, Published: 1 November 2017 Springer Science and Business Media LLC
In this work, a general two-point Ostrowski’s formula from an analytic point of view is presented. New triangle type inequalities for Riemann–Stieltjes integrals are established. Sharp two-point Ostrowski’s type inequalities for functions of bounded p-variation and functions satisfy Lipschitz condition involving $$L^p$$Lp-bounds $$(1\le p \le \infty )$$(1≤p≤∞) are proved. Some sharp inequalities ramified from the presented inequalities are also obtained.

• On Beesack–Wirtinger Inequality

Results in Mathematics, ISSN: 14226383, eISSN: 14209012, Pages: 1213-1225, Published: 1 November 2017 Springer Science and Business Media LLC
In this work, inequalities of Beesack–Wirtinger type for absolutely continuous functions whose derivatives belong to $$L_p$$Lp spaces $$p>1$$p>1 are proved. Generalizations of the results for n-times differentiable functions are established. Consequently, two Ostrowski and Čebyšev type inequalities for absolutely continuous functions whose derivatives belong to $$L^p$$Lp spaces $$p>1$$p>1 are provided.

• A generalization of Hermite-Hadamard's inequality

Kragujevac Journal of Mathematics, ISSN: 14509628, Pages: 313-328, Published: 2017 Centre for Evaluation in Education and Science (CEON/CEES)
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.

• Some Steffensen-type inequalities
Mohammad W. Alomari, Sabir Hussain, and Zheng Liu

Advances in Pure and Applied Mathematics, ISSN: 18671152, eISSN: 18696090, Pages: 219-226, Published: 2017 Walter de Gruyter GmbH
AbstractIn this paper, new inequalities connected with the celebrated Steffensen’s integral inequality are proved.

• A companion of Grüss type inequality for Riemann-Stieltjes integral and applications
Matematicki Vesnik, ISSN: 00255165, Pages: 202-212, Published: 2014

• New Grüss type inequalities for double integrals

Applied Mathematics and Computation, ISSN: 00963003, Volume: 228, Pages: 102-107, Published: 1 February 2014 Elsevier BV
In this paper, new Gruss type inequalities for double integrals are proved. Some sharp bounds are provided as well.

• New inequalities of Steffensen’s type for s-convex functions

Afrika Matematika, ISSN: 10129405, eISSN: 21907668, Pages: 1053-1062, Published: 2014 Springer Science and Business Media LLC
In this work, new inequalities connected with the Steffensen’s integral inequality for $$s$$s-convex functions are proved.

• Difference between two Riemann-Stieltjes integral means

Kragujevac Journal of Mathematics, ISSN: 14509628, Pages: 35-49, Published: 2014 Centre for Evaluation in Education and Science (CEON/CEES)
In this paper, several bounds for the dierence between two Rieman- Stieltjes integral means under various assumptions are proved.

• New grüss type inequalities for riemann-stieltjes integral with monotonic integrators and applications
Mohammad W. Alomari and Sever S. Dragomir

Annals of Functional Analysis, ISSN: 20088752, Pages: 77-93, Published: 2014 Duke University Press
In this paper several new inequalities of Grüsstype for RiemannStieltjes integral with monotonic nondecreasing integrators under various assumptions for integrands are proved. Applications for functions of selfadjoint operators on complex Hilbert spaces are provided as well. 1. Introduction The μ Cebyev functional dened by (1.1) T (f; g) = 1 b a Z b a f (t) g (t) dt 1 b a Z b a f (t) dt 1 b a Z b a g (t) dt has interesting applications in the approximation of the integral of a product as pointed out in the references below. The problem of bounding the μ Cebyev functional has a long history, starting with Grüss [21] inequality in 1935, where he had proved that for two integrable functions f; g such that f(x) and f(x) for any x 2 [a; b], the inequality (1.2) jC (f; g)j 1 4 ( ) ( ) holds, and the constant 1 4 is the best possible. After that many authors have studied the functional (1.1) and therefore, several bounds under various assumptions for the functions involved have been obtained. For some new results and generalizations the reader may refer to [1][20], [23] and the references therein. One of the recent generalization of (1.1) was considered by Dragomir in [9]. Namely, he has introduced the following μ Cebyev functional for the RiemannStieltjes integral T (f; g;u) := 1 u (b) u (a) Z b a f (t) g (t) du (t) (1.3) 1 u (b) u (a) Z b a f (t) du (t) 1 u (b) u (a) Z b a g (t) du (t) under the assumptions that f; g are continuous on [a; b] and u is of bounded variation on [a; b] with u(b) 6= u(a). 2000 Mathematics Subject Classication. 26D10, 26D15, 47A63. Key words and phrases. Grüss inequality, Functions of bounded variation, Hölder continuous functions, Riemann-Stieltjes integral. 1 2 M.W. ALOMARI AND S.S. DRAGOMIR By simple computations with the Riemann-Stieltjes integral, Dragomir [9] established the identity: T (f; g;u) = 1 u (b) u (a) Z b a f (t) f (a) + f (b) 2 (1.4) " g (t) 1 u (b) u (a) Z b a g (s) du (s) # du (t); to obtain several sharp bounds of the μ Cebyev functional for the Riemann-Stieltjes integral (1.3). In this paper, some new Grüsstype inequalities for the Riemann-Stieltjes integral with monotonic nondecreasing integrators are proved. Applications for functions of selfadjoint operators on complex Hilbert spaces via the spectral representation theorem are provided as well. 2. The Results We may start with the following result: Theorem 1. Let f : [a; b] ! C be a pHfHölder continuous function on [a; b], where p 2 (0; 1] and Hf > 0 are given. Let g; u : [a; b] ! R be such that g is RiemannStieltjes integrable with respect to a monotonic non-decreasing function u on [a; b] and there exists the real numbers ; such that g(x) for all x 2 [a; b]; then (2.1) jT (f; g;u)j 1 2p+1 Hf ( ) (b a) : Proof. Taking the modulus in (1:4) and utilizing the triangle inequality, we get jT (f; g;u)j 1 u (b) u (a) Z b a f (t) f (a) + f (b) 2 (2.2) g (t) 1 u (b) u (a) Z b a g (s) du (s) du (t) 1 u (b) u (a) sup t2[a;b] f (t) f (a) + f (b) 2 Z b a g (t) 1 u (b) u (a) Z b a g (s) du (s) du (t): Now, using the same approach considered in [11], we dene I (g) := 1 u (b) u (a) Z b a g (t) 1 u (b) u (a) Z b a g (s) du (s) !2 du (t): NEW GRÜSS TYPE INEQUALITIES 3 Then, we have I (g) = 1 u (b) u (a) Z b a " g (t) 2g (t) 1 u (b) u (a) Z b a g (s) du (s) + 1 u (b) u (a) Z b a g (s) du (s) !235 du (t)

• New Sharp Ostrowski-type Inequalities and Generalized Trapezoid-type Inequalities for Riemann-Stieltjes Integrals and their Applications
M. W. Alomari

Ukrainian Mathematical Journal, ISSN: 00415995, eISSN: 15739376, Pages: 995-1018, Published: 2013 Springer Science and Business Media LLC
We prove new sharp weighted generalizations of Ostrowski-type and generalized trapezoid-type inequalities for Riemann–Stieltjes integrals. Several related inequalities are deduced and investigated. New Simpson-type inequalities are obtained for the $\mathcal{R}\mathcal{S}$-integral. Finally, as an application, we estimate the error of a general quadrature rule for the $\mathcal{R}\mathcal{S}$-integral via the Ostrowski–generalized-trapezoid-quadrature formula.

• A companion of Ostrowski's inequality for the Riemann-Stieltjes integral ∫ ab f (t) du (t), where f is of bounded variation and u is of r-H-Hölder type and applications

Applied Mathematics and Computation, ISSN: 00963003, Volume: 219, Pages: 4792-4799, Published: 1 January 2013 Elsevier BV
Some companions of Ostrowski's integral inequality for the Riemann-Stieltjes integral @!"a^bf(t)du(t), where f is assumed to be of bounded variation on [a,b] and u is of r-H-Holder type 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.

• On approximation of the Riemann-Stieltjes integral and applications
Wajeeh Alomari

Publications de l'Institut Mathematique, ISSN: 03501302, Issue: 106, Pages: 145-156, Published: 2012 National Library of Serbia

• On Ostrowski-type inequalities for functions whose derivatives are m-convex and (α,m)-convex functions with applications
Mohammad W. Alomari, Mahmmud A. Latif, and Sabir Hussain

Tamkang Journal of Mathematics, ISSN: 00492930, Pages: 521-532, Published: December 2012 Tamkang Journal of Mathematics

• Some Grüss type inequalities for Riemann-Stieltjes integral and applications
Acta Mathematica Universitatis Comenianae, ISSN: 08629544, eISSN: 13360310, Pages: 211-220, Published: 2012

• A companion of Dragomir’s generalization of the Ostrowski inequality and applications to numerical integration
M. W. Alomari

Ukrainian Mathematical Journal, ISSN: 00415995, eISSN: 15739376, Pages: 491-510, Published: 1 September 2012 Springer Science and Business Media LLC
Some analogs of Dragomir’s generalization of the Ostrowski integral inequality$$\left| {\left( {b - a\left[ {\lambda \frac{{f(a) + f(b)}}{2} + \left( {1 - \lambda } \right)f(x)} \right] - \int\limits_a^b {f(t)dt} } \right)} \right| \leqslant \left[ {\frac{{{{\left( {b - a} \right)}^2}}}{4}\left( {\lambda^2 + {{\left( {1 - \lambda } \right)}^2}} \right) + {{\left( {x - \frac{{a + b}}{2}} \right)}^2}} \right]{\left\| {f'} \right\|_\infty }$$are established. Some sharp inequalities are proved. An application to the composite quadrature rule is provided.

• On companion of Ostrowski inequality for mappings whose first derivatives absolute value are convex with applications
Mohammad W. Alomari, M. Emin Özdemir, and Havva Kavurmac

Miskolc Mathematical Notes, ISSN: 17872405, eISSN: 17872413, Pages: 233-248, Published: 2012 Mathematical Notes
Several inequalities for a companion of Ostrowski inequality for absolutely continuous mappings whose first derivatives absolute value are convex (resp. concave) are established. Applications to a composite quadrature rule, to p.d.f.’s, and to special means are provided. 2000 Mathematics Subject Classification: 26D10; 26A15; 26A16; 26A51

• Generalized double-integral Ostrowski type inequalities on time scales
Sabir Hussain, Muhammad Amer Latif, and Mohammad Alomari

Applied Mathematics Letters, ISSN: 08939659, Pages: 1461-1467, Published: August 2011 Elsevier BV
An Ostrowski type inequality for a double integral is derived via a ΔΔ-integral on time scales; this generalizes an Ostrowski type inequality and some related results from Liu et al. (2010) [1]. Some new applications are also given.

• Some inequalities of Hermite-Hadamard type for s-convex functions
Mohammad W. Alomari, Maslina Darus, and Uğur S. Kirmaci

Acta Mathematica Scientia, ISSN: 02529602, Pages: 1643-1652, Published: July 2011 Elsevier BV
In this paper several inequalities of the left-hand side of Hermite-Hadamard's inequality are obtained for s-convex functions.

• Two inequalities of Simpson type for quasi-convex functions and applications
Applied Mathematics E - Notes, ISSN: 16072510, eISSN: 16072510, Pages: 110-117, Published: 2011

• Ostrowski type inequalities for functions whose derivatives are s-convex in the second sense
M. Alomari, M. Darus, S.S. Dragomir, and P. Cerone

Applied Mathematics Letters, ISSN: 08939659, Pages: 1071-1076, Published: September 2010 Elsevier BV
New inequalities of Ostrowski type for functions whose derivatives in absolute value are s-convex in the second sense are obtained.

• New inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are quasi-convex
Mohammad W Alomari, Maslina Darus, and Sever S. Dragomir

Tamkang Journal of Mathematics, ISSN: 00492930, Pages: 353-359, Published: Winter 2010 Tamkang Journal of Mathematics
In this note we obtain some inequalities of Hermite-Hadamardtype for functions whose second derivatives absolute values are quasi-convex.Applications for special means are also provided.

• Refinements of Hadamard-type inequalities for quasi-convex functions with applications to trapezoidal formula and to special means
M. Alomari, M. Darus, and U.S. Kirmaci

Computers and Mathematics with Applications, ISSN: 08981221, Pages: 225-232, Published: January 2010 Elsevier BV
In this paper, some inequalities of Hadamard's type for quasi-convex functions are given. Some error estimates for the Trapezoidal formula are obtained. Applications to some special means are considered.

• On hadmard-type inequalities for h-convex functions on the co-ordinates
International Journal of Mathematical Analysis, ISSN: 13128876, Issue: 33-36, Pages: 1645-1656, Published: 2009

• On the hadamards inequality for log-convex functions on the coordinates
Mohammad Alomari and Maslina Darus

Journal of Inequalities and Applications, ISSN: 10255834, eISSN: 1029242X, Volume: 2009, Published: 2009 Springer Science and Business Media LLC
Inequalities of the Hadamard and Jensen types for coordinated log-convex functions defined in a rectangle from the plane and other related results are given.

## RECENT SCHOLAR PUBLICATIONS

• On Cauchy-Schwarz type inequalities and applications to numerical radius inequalities
MW Alomari
arXiv preprint arXiv:2009.01839 2020

• Two-point Ostrowski and Ostrowski–Grss type inequalities with applications
MW Alomari
The Journal of Analysis 28 (3), 623-661 2020

• On the Davis-Wielandt radius inequalities of Hilbert space operators
MW Alomari
arXiv preprint arXiv:2008.00758 2020

• A Generalization of weighted companion of Ostrowski integral inequality for mappings of bounded variation
MW Alomari
International Journal of Nonlinear Sciences and Numerical Simulation 1 2020

• The generalized Schwarz inequality for semi-Hilbertian space operators and Some -numerical radius inequalities
MW Alomari
arXiv preprint arXiv:2007.01701 2020

• Klein's trace inequality and superquadratic trace functions
M Kian, MW Alomari
arXiv preprint arXiv:2001.10013 2020

• On Some Inequalities for the Generalized Euclidean Operator Radius
M Alomari
Preprints 2019

• On the Dragomir Extension of Furuta's Inequality and Numerical Radius Inequalities
M Alomari
Preprints 2019

• Improvements of some numerical radius inequalities
MW Alomari
arXiv preprint arXiv:1912.01492 2019

• Some properties of h-MN-convexity and Jensen’s type inequalities
MW Alomari
Journal of Interdisciplinary Mathematics 22 (8), 1349-1395 2019

• Bounds for the difference between two Čebyšev functionals
MW Alomari
Afrika Matematika, 1-18 2019

• Operator Popoviciu’s inequality for superquadratic and convex functions of selfadjoint operators in Hilbert spaces
MW Alomari
Advances in Pure and Applied Mathematics 10 (4), 313-324 2019

• Refinements of some numerical radius inequalities for Hilbert space operators
MW Alomari
Linear and Multilinear Algebra, 1-16 2019

• On Pompeiu–Chebyshev functional and its generalization
MW Alomari
Results in Mathematics 74 (1), 56 2019

• Operator Jensen's inequality for operator superquadratic functions
MW Alomari
arXiv preprint arXiv:1902.04894 2019

• OPERATOR JENSEN’S INEQUALITY FOR OPERATOR SUPERQUADRATIC WITH APPLICATIONS TO QUASI-ARITHMETIC MEANS
MW ALOMARI, J MICIC
arXiv preprint arXiv:1902.04894 2019

• A note on h-convex functions
MW Alomari
e-Journal of Analysis and Applied Mathematics 2019 (1), 55-67 2019

• Sharp Wirtinger's type inequalities for double integrals with Applications
MW Alomari
arXiv preprint arXiv:1812.06130 2018

• Two-Point Quadrature Rules for Riemann–Stieltjes Integrals with Lp–error estimates
MW Alomari
Moroccan Journal of Pure and Applied Analysis 4 (2), 94-109 2018

• Some Numerical radius inequalities
MW Alomari
arXiv preprint arXiv:1811.08025 2018

## 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: 175

• The Hadamard’s inequality for s-convex function of 2-variables on the co-ordinates
M Alomari, M Darus
International Journal of Math. Analysis 2 (13), 629-638 2008
Citations: 150

• 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: 126

• On the Hadamard's inequality for log-convex functions on the coordinates
M Alomari, M Darus
Journal of Inequalities and Applications 2009 (1), 283147 2009
Citations: 123

• New inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are quasi-convex
MW Alomari, M Darus, SS Dragomir
Tamkang Journal of Mathematics 41 (4), 353-359 2010
Citations: 117

• 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: 110

• 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: 108

• 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: 104

• On Hadamard-type inequalities for h-convex functions on the co-ordinates
MA Latif, M Alomari
Int. J. of Math. Analysis 3 (33), 1645-1656 2009
Citations: 95

• Hadamard-type inequalities for s-convex functions
M Alomari, M Darus
Int. Math. Forum 3 (37-40), 1965-1975 2008
Citations: 83

• Integral inequalities via several kinds of convexity
ME zdemir, E Set, M Alomari
Creat. Math. Inform 20 (1), 62-73 2011
Citations: 73

• 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: 67

• 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: 64

• Some Ostrowski type inequalities for quasi-convex functions with applications to special means
M Alomari, M Darus
RGMIA Res. Rep. Coll 13 (2) 2010
Citations: 59

• 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: 43

• Generalized double-integral Ostrowski type inequalities on time scales
S Hussain, MA Latif, M Alomari
Applied Mathematics Letters 24 (8), 1461-1467 2011
Citations: 41

• Two inequalities of Simpson type for quasi-convex functions and applications
M Alomari, S Hussain
Appl. Math. E-Notes 11, 110-117 2011
Citations: 41

• A companion of Ostrowski’s inequality with applications
MW Alomari
Transylv. J. Math. Mech 3 (1), 9-14 2011
Citations: 40

• 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: 36

• 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: r's generalization of Ostrowski's inequality and applications in numerical integration