On Generalized Simultaneous Nearest Point in Normed Spaces

Abstract

In this paper, we study the problem of generalized simultaneous approximation in terms of the Minkowski functional. We develop a theory of generalized best simultaneous approximation in quotient spaces and introduce equivalent assertions between the subspaces $W$ and $W+M$ and the quotient space $W/M$. Some other results regarding generalized simultaneous approximation in Banach space are presented.