Ky Fan Type Best Approximation Theorem for a Class of Factorizable Multifunctions (Analysis in Theory and Applications, 2012)
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.
Keywords: Almost affine; almost quasi convex; approximately weakly compact; best approximation; demicontinuous map; locally convex space; relative almost quasi convex; Kakutani factorizable multifunction; upper semicontinuous map.