Convex subsets

Xem 1-6 trên 6 kết quả Convex subsets
  • The intent of this book is to set the modern foundations of the theory of generalized curvature measures. This subject has a long history, beginning with J. Steiner (1850), H. Weyl (1939), H. Federer (1959), P. Wintgen (1982), and continues today with young and brilliant mathematicians. In the last decades, a renewal of interest in mathematics as well as computer science has arisen (finding new applications in computer graphics, medical imaging, computational geometry, visualization …).

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  • In this paper we study Lipschitz solutions of partial differential relations of the form (1) ∇u(x) ∈ K a.e. in Ω, where u is a (Lipschitz) mapping of an open set Ω ⊂ Rn into Rm , ∇u(x) is its gradient (i.e. the matrix ∂ui (x)/∂xj , 1 ≤ i ≤ m, 1 ≤ j ≤ n, defined for almost every x ∈ Ω), and K is a subset of the set M m×n of all real m × n matrices. In addition to relation (1), boundary conditions and other conditions on u will also be considered. Relation (1)...

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  • We prove that the classical Oka property of a complex manifold Y, concerning the existence and homotopy classification of holomorphic mappings from Stein manifolds to Y, is equivalent to a Runge approximation property for holomorphic maps from compact convex sets in Euclidean spaces to Y . Introduction Motivated by the seminal works of Oka [40] and Grauert ([24], [25], [26]) we say that a complex manifold Y enjoys the Oka property if for every Stein manifold X, every compact O(X)-convex subset K of X and every continuous map f0 : X → Y which is holomorphic in an...

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  • MANN ITERATION CONVERGES FASTER THAN ISHIKAWA ITERATION FOR THE CLASS OF ZAMFIRESCU OPERATORS G. V. R. BABU AND K. N. V. V. VARA PRASAD Received 3 February 2005; Revised 31 March 2005; Accepted 19 April 2005 The purpose of this paper is to show that the Mann iteration converges faster than the Ishikawa iteration for the class of Zamfirescu operators of an arbitrary closed convex subset of a Banach space. Copyright © 2006 Hindawi Publishing Corporation. All rights reserved. 1. Introduction Let E be a normed linear space, T : E → E a given operator. Let x0 ∈ E be arbitrary...

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  • Abstract. The classical Heron problem states: on a given straight line in the plane, find a point C such that the sum of the distances from C to the given points A and B is minimal. This problem can be solved using standard geometry or differential calculus. In the light of modern convex analysis, we are able to investigate more general versions of this problem. In this paper we propose and solve the following problem: on a given nonempty closed convex subset of Rs , find a point such that the sum of the distances from that point to n given nonempty closed convex subsets of...

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  • In this paper we give results about polynomial approximation on the closed polydisk in Cn . 1. Introduction Let X be a compact subset of Cn . By C(X) we denote the space of all continuous complex-valued functions on X, with norm f X = max{|f (z)| : z ∈ X}, and let P (X) denote the closure of set of polynomials in C(X). The polynomially convex hull of X will ˆ be denoted by X and difined by ˆ X = {z ∈ Cn : |p(z)| p X for every polynomial p}.

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