Approximation and Fixed-Point Theorems for Condensing Composites of Multifunctions

One of the authors previously extended an interesting best approximation. theorey of Ky Fan to condensing maps defined on a closed ball in a Banach space and defined on a closed convex subset in a Hilbert space. Recently there have appeared a number of new results on fixed points of so-called Kakutani factorizable multifunctions or composites of acyclic or other type of multifunctions defined on convex subsets of topological vector spaces. In this paper, we extend Lin’s results to the multifunction or set-valued.version for the above-mentioned factorizable multifunctions. Applications to fixed-point theorems are given