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- R R Phelps, S Simons
- 2007

Many of the most useful results concerning maximal monotone set{valued operators are only valid in reeexive Banach spaces. In an eeort to extend some of these results to nonreeexive spaces, various authors have introduced certain natural subclasses of maximal monotone operators (subclasses which are identical with the entire class of maximal monotone… (More)

- R R Phelps
- 1997

Introduction. These lectures will focus on those properties of maximal monotone operators which are valid in arbitrary real Banach spaces. Most applications (to nonlinear partial differential equations, optimization, calculus of variations, etc.) take place in reflexive spaces, in part because several key properties have only been shown to hold in such… (More)

- R. R. PHELPS, A. L. Garkavi
- 2010

1. Introduction. If £ is a real normed linear space, a subspace M of E is said to be a CebySev subspace ii to each y in E there exists a unique nearest element x in M, that is, an element x in M such that ||y—x|| <||y—z\\ for zEM, z^x. The problem of characterizing such subspaces for the classical Banach spaces of functions is an interesting one. The first… (More)

- R. R. PHELPS
- 2010

A corollary of the Bishop-Phelps theorem is that a closed convex subset C of a Banach space can always be represented as the intersection of its supporting closed half-spaces. In this paper an investigation is made of those subsets S of C such that C is the intersection of those closed half-spaces which support it at points of C\S. This will be true for… (More)

- A. S. Granero, J. P. Moreno, R. R. Phelps
- Discrete & Computational Geometry
- 2004

We deal with some problems related to vector addition and diametric completion procedures of convex bodies in C(K) spaces. We prove that each of the following properties of convex bodies in C(K) characterizes the underlying compact Hausdorff space K as a Stonean space: (i) C(K) has a generating unit ball; (ii) all Maehara sets in C(K) are complete; (iii)… (More)

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