We prove some results on operator equalities and inequalities involving positive maps, operator means and shorted operators. Inequalities for shorted operators involving convex operator functions and tensor product have also been proved.

In this paper we present a new fixpoint-based approach to bottom-up state generation for stratifiable disjunctive deductive databases. To this end, a new consequence operator based on hyperresolution is introduced which extends Minker’s operator for positive disjunctive Datalog rules. In contrast to already existing model generation methods our approach for efficiently computing perfect models ...

Let $\varphi=\{\varphi_k\}_{k=-\infty}^\infty$ denote the extended Takenaka--Malmquist system on unit circle $\mathbb T$ and let $\sigma_{n,\varphi}(f),$ $f\in L^1(\mathbb T)$, be Fej\'er-type operator based $\varphi$, introduced by V. N. Rusak. We give convergence criteria for $\sigma_{n,\varphi}(f)$ in Banach space $X(\mathbb T):=L^p(\mathbb T)\vee C(\mathbb $p\ge 1$. Also we prove Voronovska...

We present two general sequences of positive linear operators. The first is introduced by using a class of dependent random variables, and the second is a mixture between two linear operators of discrete type. Our goal is to study their statistical convergence to the approximated function. This type of convergence can replace classical results provided by Bohman-Korovkin theorem. A particular c...