Results 31 to 40 of about 1,126,628 (203)
Preliminaries on CAT (0) Spaces and Fixed Points of a Class of Iterative Schemes [PDF]
arXiv, 2016 This paper gives some relating results for various concepts of convexity in metric spaces such as midpoint convexity, convex structure, uniform convexity and near-uniform convexity, Busemann curvature and its relation to convexity. Some properties of uniform convexity and near uniform convexity of geodesic metric spaces are related to the mapping built
arxiv
Convexity of momentum maps: A topological analysis [PDF]
Topology and its Applications, 2012 The Local-to-Global-Principle used in the proof of convexity theorems for momentum maps has been extracted as a statement of pure topology enriched with a structure of convexity. We extend this principle to not necessarily closed maps $f\colon X\ra Y$ where the convexity structure of the target space $Y$ need not be based on a metric.
Jenny Santoso, Wolfgang Rump
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, 2016 Recently, based on the idea of randomizing space theory, random convex analysis has been being developed in order to deal with the corresponding problems in random environments such as analysis of conditional convex risk measures and the related variational problems and optimization problems.
Guo, Tiexin +5 more
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Sharp trace Gagliardo-Nirenberg-Sobolev inequalities for convex cones, and convex domains [PDF]
arXiv, 2017 We find a new sharp trace Gagliardo-Nirenberg-Sobolev inequality on convex cones, aswell as a weighted sharp trace Sobolev inequality on epigraphs of convex functions. This is done by using a generalized Borell-Brascamp-Lieb inequality, coming from the Brunn-Minkowski theory.
arxiv
Duality and calculi without exceptions for convex objects [PDF]
The aim of this paper is to make a contribution to theinvestigation of the roots and essence of convex analysis, and tothe development of the duality formulas of convex calculus.
Brinkhuis, J.
core +1 more source
Global approximation of convex functions by differentiable convex functions on Banach spaces [PDF]
arXiv, 2014 We show that if $X$ is a Banach space whose dual $X^{*}$ has an equivalent locally uniformly rotund (LUR) norm, then for every open convex $U\subseteq X$, for every $\varepsilon >0$, and for every continuous and convex function $f:U \rightarrow \mathbb{R}$ (not necessarily bounded on bounded sets) there exists a convex function $g:X \rightarrow \mathbb{
arxiv
, 2020 Convexity is an important notion in non linear optimization theory as well as in infinite dimensional functional analysis. As will be seen below, very simple and powerful tools will be derived from elementary duality arguments (which are byproducts of the Moreau-Fenchel transform and Hahn Banach Theorem).
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Convex-transitivity and function spaces [PDF]
arXiv, 2007 If X is a convex-transitive Banach space and 1\leq p\leq \infty then the closed linear span of the simple functions in the Bochner space L^{p}([0,1],X) is convex-transitive. If H is an infinite-dimensional Hilbert space and C_{0}(L) is convex-transitive, then C_{0}(L,H) is convex-transitive. Some new fairly concrete examples of convex-transitive spaces
arxiv
On a conic approach to convex analysis. [PDF]
. The aim of this paper is to make an attempt to justify the main results from Convex Analysis by one elegant tool, the conification method, which consists of three steps: conify, work with convex cones, deconify.
Brinkhuis, J.
core +1 more source
Operator log-convex functions and f-divergence functional [PDF]
arXiv, 2013 We present a characterization of operator log-convex functions by using positive linear mappings. Moreover, we study the non-commutative f-divergence functional of operator log-convex functions. In particular, we prove that f is operator log-convex if and only if the non-commutative f-divergence functional is operator log-convex in its first variable ...
arxiv