arXiv subjects
Publications and source records attributed to Mohammad W. Alomari.
In this work, sharp Wirtinger type inequalities for double integrals are established. As applications, two sharp Čebyšev type inequalities for absolutely continuous functions whose second partial derivatives belong to $L^2$ space are proved.
In this work, generalizations of some inequalities for continuous $h$-synchronous ($h$-asynchronous) functions of linear bounded selfadjoint operators under positive linear maps in Hilbert spaces are proved.
In this work, a pre-Grüss inequality for positive Hilbert space operators is proved. So that, some numerical radius inequalities are proved. On the other hand, based on a non-commutative Binomial formula, a non-commutative upper bound for the numerical radius of the summand of two bounded linear Hilbert space operators is proved. A commutative version is also obtained as well.
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.
In this work, operator version of Popoviciu's inequality for positive selfadjoint operators in Hilbert spaces under positive linear maps for superquadratic functions is proved. Analogously, using the same technique operator version of Popoviciu's inequality for convex functions is obtained. Some other related inequalities are also deduced.
In this work, the q-analogue of Bernoulli inequality is proved. Some other related results are presented.
In this work, generalization of some inequalities for continuous $h$-synchronous ($h$-asynchronous) functions of selfadjoint linear operators in Hilbert spaces are proved.
In this work, a generalization of Chebyshev functional is presented. New inequalities of Gruss type via Pompeiu's mean value theorem are established. Improvements of some old inequalities are proved. A generalization of pre-Gruss 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 [a,b] under some other circumstances are introduced. Other related ramified inequalities for differentiable functions are also given.
Extensions and generalizations of Alzer's inequality; which is of Wirtinger type are proved. As applications, sharp trapezoid type inequality and sharp bound for the geometric mean are deduced.
In this work, an expansion of Guessab-Schmeisser two points formula for n-times differentiable functions via Fink type identity is established. Generalization of the main result for harmonic sequence of polynomials is established. Several bounds of the presented results are proved. As applications, some quadrature rules are elaborated and discussed. Error bounds of the presented quadrature rules via Chebyshev-Gruss type inequalities are also provided.
In this work, approximations for real two variables function $f$ which has continuous partial $(n-1)$-derivatives $(n \ge 1)$ and has the $n$--th partial derivative of bounded bivariation or absolutely continuous are established. Explicit bounds for this representation are given. An approximation of a function $f$ by its mid-point formula with its error is established.
Given any ${\bf{a}}: = \left( {a_1 ,a_2 , \ldots ,a_n } \right)$ and ${\bf{b}}: = \left( {b_1 ,b_2 , \ldots ,b_n } \right)$ in $\mathbb{R}^n$. The $\textbf{n}$-fold convex function defined on $\left[ {\bf{a},{\bf{b}}} \right]$, ${\bf{a}},{\bf{b}} \in \mathbb{R}^n$ with ${\bf{a}}<{\bf{b}}$ is a convex function in each variable separately. In this work we prove an inequality of Hermite-Hadamard type for $\textbf{n}$-fold convex functions. Namely, we establish the inequality \begin{align*} f\left( {\frac{{\bf{a} + {\bf{b}}}}{2}} \right) \le \frac{1}{{\bf{b} - {\bf{a}}}}\int_{\bf{a}}^{\bf{b}} {f\left( {\bf{x}} \right)d{\bf{x}}} \le \frac{1}{2^n }\sum\limits_{\bf{c}} {f\left( {\bf{c}} \right)}, \end{align*} where $\sum\limits_{\bf{c}} {f\left( {\bf{c}} \right)} : = \sum\limits_{\mathop {c_i \in \left\{ {a_i ,b_i } \right\}}\limits_{1 \le i \le n} } {f\left( {c_1, c_2, \ldots ,c_n } \right)}$. Some other related result are given.
In this work, new inequalities connected with the Steffensen's integral inequality for s-convex functions are proved
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.
In this paper, an inequality of Simpson type for quasi-convex mappings are proved. The constant in the classical Simpson's inequality is improved. Furthermore, the obtained bounds can be (much) better than some recently obtained bounds. Application to Simpson's quadrature rule is also given.
In this paper, new upper and lower bounds for the Trapezoid inequality of absolutely continuous functions are obtained. Applications to some special means are provided as well.
In this paper, new sharp weighted generalizations of Ostrowski and generalized trapezoid type inequalities for the Riemann--Stieltjes integrals are proved. Several related inequalities are deduced and investigated. New Simpson's type inequalities for $\mathcal{RS}$--integral are pointed out. Finally, as application; an error estimation of a general quadrature rule for $\mathcal{RS}$--integral via Ostrowski--generalized trapezoid quadrature formula is given.
In order to approximate the Riemann--Stieltjes integral $\int_a^b {f\left( t \right)dg\left( t \right)}$ by $2$--point Gaussian quadrature rule, we introduce the quadrature rule \begin{align*} \int_{ - 1}^1 {f\left( t \right)dg\left( t \right)} \approx A f\left( { - \frac{\sqrt 3 }{3}} \right) + B f\left( {\frac{\sqrt 3 }{3}} \right), \end{align*} for suitable choice of $A$ and $B$. Error estimates for this approximation under various assumptions for the functions involved are provided as well.