EXISTENCE RESULTS ON BEST PROXIMITY PAIR IN METRIZABLE TOPOLOGICAL VECTOR SPACES

Abstract

In this paper, an existence result on best proximity pair is proved. For this purpose, a closed convex upper semi-continuous multifunctions and the other one being a demicontinuous, relative almost quasi-convex, onto function on an approximately weakly compact, convex subset of metrizable topological vector space are used. This result generalizes the result of Basha and Veeramani [10]. Finally, certain known results have also been obtained as corollaries in this work.