KY FAN TYPE BEST APPROXIMATION THEOREM FOR A CLASS OF FACTORIZABLE MULTIFUNCTIONS

An existence result on Ky Fan type best approximation is proved. For this purpose, a class of factorizable multifunctions and the other one being a demicontinuous, relative almost quasi-convex, onto function on an approximately weakly compact, convex subset of Hausdorff locally convex topological vector space are used. As consequence, this result extends the best approximation results of Basha and Veeramani [8] and many others.     

Fixed points for convex continuous mappings in topological vector spaces

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