Let {Xn ,n=>1} be a strictly stationary sequence of negatively associated random variables, with common distribution function F. In this paper, we consider the estimation of the two-dimensional distribution function of (X1, Xk+1) for fixed $K /in N$ based on kernel type estimators. We introduce asymptotic normality and properties and moments. From these we derive the optimal bandwidth...

We investigate strictly positive finitely additive measures on Boolean algebras and strictly positive Radon measures on compact zerodimensional spaces. The motivation is to find a combinatorial characterisation of Boolean algebras which carry a strictly positive finitely additive finite measure with some additional properties, such as separability or nonatomicity. A possible consistent characte...

The square root function has a unique positive ¿xed point. This function has the following properties: it is strictly increasing and strictly concave, with sEf ' f, sE@ : @ for @ , and sEK K for K : . It is shown that any function from U to U satisfying these properties has a unique positive ¿xed point.

We consider maps fK(v) = minA∈K Av and gK(v) = maxA∈KAv, where K is a finite set of nonnegative matrices and by “min” and “max” we mean component-wise minimum and maximum. We transfer known results about properties of gK to fK. In particular we show existence of nonnegative generalized eigenvectors of fK, give necessary and sufficient conditions for existence of strictly positive eigenvector of...

We prove that if K is a Gruenhage compact space then C (K) admits an equivalent, strictly convex dual norm. As a corollary, we show that if X is a Banach space and X∗ = span|||·|||(K), where K is a Gruenhage compact in the w∗-topology and ||| · ||| is equivalent to a coarser, w∗-lower semicontinuous norm on X∗, then X∗ admits an equivalent, strictly convex dual norm. We give a partial converse ...

Let nd,k be the largest order of a directed graph (digraph) with given maximum out-degree d and diameter k. In this note we show that nd,k is strictly monotonic increasing in each of d and k.

We consider functions f v = min A∈K Av and gv = max A∈K Av, where K is a finite set of nonnegative matrices and by " min " and " max " we mean coordinate-wise minimum and maximum. We transfer known results about properties of g to f. In particular we show existence of nonnegative generalized eigenvectors for f , give necessary and sufficient conditions for existence of strictly positive eigenve...

In this paper, we prove the ∆-convergence theorems of the cyclic algorithm and the new multi-step iteration for k-strictly pseudo-contractive mappings and give also the strong convergence theorem of the modified Halpern’s iteration for these mappings in a CAT (0) space. Our results extend and improve the corresponding recent results announced by many authors in the literature. Key–Words: CAT (0...