arXiv subjects
Publications and source records attributed to M. W. Alomari.
In this work, we show that the proof of the main result in [An Application of Hayashi's Inequality for Differentiable Functions, Computers & Mathematics with Applications, 32 (6) (1996), 95--99, by R.P. Agarwal and S.S. Dragomir] was wrong. A correction of the proof is given. More general related inequalities are also provided.
In this work, an operator superquadratic function (in 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. Equivalent statements of a non-commutative version of Jensen's inequality for operator superquadratic function are established. A generalization of the main result to any positive unital linear map is also provided.
In this work, we discuss the continuity of $h$-convex functions by introducing the concepts of $h$-convex curves ($h$-cord). Geometric interpretation of $h$-convexity is given. The fact that for a $h$-continuous function $f$, is being $h$-convex if and only if is $h$-midconvex is proved. Generally, we prove that if $f$ is $h$-convex then $f$ is $h$-continuous. A discussion regarding derivative characterization of $h$-convexity is also proposed.
In this work, Lp-error estimates of general two and three point quadrature rules for Riemann-Stieltjes integrals are give n. The presented proofs depend on new triangle type inequalities of Riemann-Stieltjes integrals
A generalization of Mercer inequality for h-convex function is presented. As application, a weighted generalization of triangle inequality is given.
In this paper, new inequalities connected with the celebrated Steffensen's integral inequality are proved.