منابع مشابه
Zone diagrams in compact subsets of uniformly convex normed spaces
A zone diagram is a relatively new concept which has emerged in computational geometry and is related to Voronoi diagrams. Formally, it is a fixed point of a certain mapping, and neither its uniqueness nor its existence are obvious in advance. It has been studied by several authors, starting with T. Asano, J. Matoušek and T. Tokuyama, who considered the Euclidean plane with singleton sites, and...
متن کاملOn Integrated Convex Optimization in Normed Linear Space
Abstract In this paper, the concept of generalized saddle point(GSP) is employed to discuss the optimization problems of a set of convex functions on a normed linear space X , which presents an equivalence under a special condition between GSP and its optimum solution. A study on integrated convex optimization problem by using Gâteaux and Fréchet differentiability respectivly, and the equivalen...
متن کاملCompactly Epi-lipschitzian Convex Sets and Functions in Normed Spaces
The concept of compactly epi-Lipschitzian (CEL) sets in locally convex topological spaces was introduced by Borwein and Strojwas [6]. It is an extension of Rockafellar’s concept of epi-Lipschitzian sets [36]. An advantage of the CEL property is that it always holds in finite dimensional spaces and, in contrast to its epi-Lipschitzian predecessor, makes it possible to recapture much of the detai...
متن کاملPorosity of Convex Nowhere Dense Subsets of Normed Linear Spaces
and Applied Analysis 3 Definition 2.4. M is called c-porous if for any x ∈ X and every r > 0, there are y ∈ B x, r and φ ∈ X∗ \ {0} such that { z ∈ X : φ z > φy ∩M ∅. 2.2 C-porosity turns out to be the suitable notion to describe the smallness of convex nowhere dense sets see Proposition 2.5 and is a stronger form of 0-angle porosity x ∈ X instead x ∈ M . Indeed, consider the unit sphere S of a...
متن کاملOuter Γ-convex Functions on a Normed Space
For some given positive γ, a function f is called outer γ-convex if it satisfies the Jensen inequality f(zi) ≤ (1 − λi)f(x0) + λif(x1) for some z0 : = x0, z1, ..., zk : = x1 ∈ [x0, x1] satisfying ‖zi − zi+1‖ ≤ γ, where λi : = ‖x0 − zi‖/‖x0 − x1‖, i = 1, 2, ..., k − 1. Though the Jensen inequality is only required to hold true at some points (although the location of these points is uncertain) o...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1972
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1972-0313769-9