Let D be a convex domain in C. Let ak > 0 be summable constants and let zk ∈ D. If the zk converge sufficiently rapidly to η ∈ ∂D from within an appropriate Stolz angle then the function ∑ ∞ k=1 ak/(z − zk) has infinitely many zeros in D. An example shows that the hypotheses on the zk are not redundant, and that two recently advanced conjectures are false. M.S.C. 2000 classification: 30D35, 31A...

and Applied Analysis 3 Definition 2.2 see 22 . Let E,D;Γ be an abstract convex space. If a mapping G : D → 2 satisfies

In Moral, Campos (1991) and Cano, Moral, Verdegay-L6pez (1991) a new method of con­ ditioning convex sets of probabilities has been proposed. The result of it is a convex set of non-necessarily normalized probability dis­ tributions. The normalizing factor of each probability distribution is interpreted as the possibility assigned to it by the conditioning information. From this, it is deduced ...

We consider a digital fuzzy set placed in Oxyplane, with support which is a set of digital points (centroids) in Z. We consider two kinds of convexity of a fuzzy set, namely quasi convexity and strong convexity, and we propose two algorithms for the construction of both kinds of convex hull of a digital fuzzy set.

Given a natural correspondence between a family of inequalities and a closed convex set in a topological linear space, one might expect that an inequality corresponding to a special point (e.g., an extreme point) would be of special interest in view of the convex analysis theory. In this paper, we realize this concept. Let X be an arbitrary set and {φ0,φ1,φ} a triple of nonnegative real-valued ...

A set X IR d is n-convex if among any n its points there exist two such that the segment connecting them is contained in X. Perles and Shelah have shown that any closed (n + 1)-convex set in the plane is the union of at most n 6 convex sets. We improve their bound to 18n 3 , and show a lower bound of order (n 2). We also show that if X IR 2 is an n-convex set such that its complement has one-po...

Let C be a closed convex subset of a Banach space E. A mapping T on C is called a nonexpansive mapping if ‖Tx−Ty‖ ≤ ‖x− y‖ for all x, y ∈ C. We denote by F(T) the set of fixed points of T . Kirk [17] proved that F(T) is nonempty in the case that C is weakly compact and has normal structure. See also [2, 3, 5, 6, 11] and others. Convergence theorems to fixed points are also proved by many author...

We deal with different properties of a smooth and strictly convex body that depend on the behavior of the planar sections of the body parallel to and close to a given tangent plane. The first topic is boundary points where any given convex domain in the tangent plane can be approximated by a sequence of suitably rescaled planar sections (so-called p-universal points). In the second topic, the g...

We focus on the problem of minimizing a convex function f over a convex set S given T queries to a stochastic first order oracle. We argue that the complexity of convex minimization is only determined by the rate of growth of the function around its minimizer xf,S , as quantified by a Tsybakov-like noise condition. Specifically, we prove that if f grows at least as fast as ‖x − xf,S‖ around its...