Remarks on quasi-variational inequalities and fixed points in locally convex topological vector spaces

Fixed Points for Convex Continuous Mappings in Topological Vector Spaces

We prove the following result. Let C be a convex compact subset in a topological vector space, and T : C → C a convex continuous mapping. (See Definition 1.1.) Then T has a fixed point. Moreover, continuous mappings that can be approximated by convex continuous mappings also have the fixed point property.

Notes on Locally Convex Topological Vector Spaces

Notes from a 1994–95 graduate course. Designed to supplement the topological vector space chapters of Rudin's Functional Analysis.

Solutions of variational inequalities on fixed points of nonexpansive mappings

n this paper , we propose a generalized iterative method forfinding a common element of the set of fixed points of a singlenonexpannsive mapping and the set of solutions of two variationalinequalities with inverse strongly monotone mappings and strictlypseudo-contractive of Browder-Petryshyn type mapping. Our resultsimprove and extend the results announced by many others.

Generalized Vector Variational Inequalities in Topological Vector Spaces

The solvability of the generalized weak vector implicit variational inequality problem, generalized strong vector implicit variational inequality problem and generalized vector variational inequality problem are proved by using a generalized Fan’s KKM theorem. Our results extend and unify corresponding results of other authors.

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points