scholarly journals Nonlinear variational inequalities on reflexive Banach spaces and topological vector spaces

2003 ◽  
Vol 2003 (4) ◽  
pp. 199-207 ◽  
Author(s):  
Zeqing Liu ◽  
Jeong Sheok Ume ◽  
Shin Min Kang
Keyword(s):  
Variational Inequalities ◽  
Banach Spaces ◽  
Vector Spaces ◽  
Reflexive Banach Spaces ◽  
Topological Vector Spaces

The purpose of this paper is to introduce and study a class of nonlinear variational inequalities in reflexive Banach spaces and topological vector spaces. Based on the KKM technique, the solvability of this kind of nonlinear variational inequalities is presented. The obtained results extend, improve, and unify the results due to Browder, Carbone, Siddiqi, Ansari, Kazmi, Verma, and others.

scholarly journals Order preserving functions on ordered topological vector spaces

1999 ◽  
Vol 60 (1) ◽  
pp. 55-65 ◽  
Author(s):  
J.C. Candeal ◽  
E. Induráin ◽  
G.B. Mehta
Keyword(s):  
Banach Spaces ◽  
Vector Spaces ◽  
Reflexive Banach Spaces ◽  
Representation Theorems ◽  
Mackey Topology ◽  
Topological Vector Spaces ◽  
Infinite Dimensional ◽  
Total Preorder

In this paper we prove the existence of continuous order preserving functions on ordered topological vector spaces in an infinite-dimensional setting. In a certain class of topological vector spaces we prove the existence of topologies for which every continuous total preorder has a continuous order preserving representation and show that the Mackey topology is the finest topology with this property. We also prove similar representation theorems for reflexive Banach spaces and for Banach spaces that may not have a pre-dual.

An Embedding Theorem for Separable Locally Convex Spaces

1971 ◽  
Vol 14 (1) ◽  
pp. 119-120 ◽  
Author(s):  
Robert H. Lohman
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Convex Space ◽  
Separable Banach Space ◽  
Locally Convex Space ◽  
Embedding Theorem ◽  
Vector Spaces ◽  
Locally Convex Spaces ◽  
Topological Vector Spaces ◽  
Locally Convex

A well-known embedding theorem of Banach and Mazur [1, p. 185] states that every separable Banach space is isometrically isomorphic to a subspace of C[0, 1], establishing C[0, 1] as a universal separable Banach space. The embedding theorem one encounters in a course in topological vector spaces states that every Hausdorff locally convex space (l.c.s.) is topologically isomorphic to a subspace of a product of Banach spaces.

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