The Dual Normal CHIP and Linear Regularity for Infinite Systems of Convex Sets in Banach Spaces

2014 ◽  
Vol 24 (3) ◽  
pp. 1075-1101 ◽  
Author(s):  
Chong Li ◽  
K. F. Ng
Keyword(s):  
Banach Spaces ◽  
Convex Sets ◽  
Infinite Systems ◽  
Linear Regularity

scholarly journals Linear Regularity for a Collection of Subsmooth Sets in Banach Spaces

2008 ◽  
Vol 19 (1) ◽  
pp. 62-76 ◽  
Author(s):  
Xi Yin Zheng ◽  
Kung Fu Ng
Keyword(s):  
Banach Spaces ◽  
Linear Regularity

Porosity and the bounded linear regularity property

2014 ◽  
Vol 20 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Simeon Reich ◽  
Alexander J. Zaslavski
Keyword(s):  
Hilbert Space ◽  
Convex Sets ◽  
Regularity Property ◽  
Nonempty Intersection ◽  
Normed Spaces ◽  
Infinite Products ◽  
Bounded Linear ◽  
Linear Regularity ◽  
Nearest Point ◽  
Convex Subsets

Abstract.H. H. Bauschke and J. M. Borwein showed that in the space of all tuples of bounded, closed, and convex subsets of a Hilbert space with a nonempty intersection, a typical tuple has the bounded linear regularity property. This property is important because it leads to the convergence of infinite products of the corresponding nearest point projections to a point in the intersection. In the present paper we show that the subset of all tuples possessing the bounded linear regularity property has a porous complement. Moreover, our result is established in all normed spaces and for tuples of closed and convex sets, which are not necessarily bounded.

scholarly journals A Characterization of Polynomially Convex Sets in Banach Spaces

2017 ◽  
Vol 72 (4) ◽  
pp. 2013-2021
Author(s):  
Mortaza Abtahi ◽  
Sara Farhangi
Keyword(s):  
Banach Spaces ◽  
Convex Sets ◽  
Polynomially Convex

(I)-envelopes of closed convex sets in Banach spaces

2007 ◽  
Vol 162 (1) ◽  
pp. 157-181 ◽  
Author(s):  
Ondřej F. K. Kalenda
Keyword(s):  
Banach Spaces ◽  
Convex Sets
Sign in / Sign up

Export Citation Format

Share Document