BEST APPROXIMATION AND BEST CO - APPROXIMATION IN CONE - NORMED SPACE

Abstract

In this thesis, the concept of Best Approximation and Best Co-Approximation in cone – normed spaces are studied. We noticed similarities between Best Approximation and Best Co–Approximation in cone–normed spaces. We obtained new results among which, we proved that: 1. We can apply Best Approximation and Best Co-Approximation theorems in normed space to cone-normed space. 2. Best Co-Approximation in cone-normed space is a counter copy of Best Approximation in cone-normed space. The concept of Proximinal additivity and ᶲc-Summand in cone–normed space are introduced. Also we have answered some questions about them.