Best Approximation and Best Co-approximation in Metric Linear Space and Normed Linear Space

Abstract

Approximation theory is an old and rich branch of analysis and a large number of researchers have studied this subject. The theory has many applications in mathematical analysis, nonlinear problems arising in physical sciences, engineering and social sciences. Since the particular examples of approximation often arise from the problems of Science and Technology, they provide proper motivation for the subject of Approximation Theory. In this work, we consider the problem of characterization, existence and uniqueness of best approximation and best co-approximation in the setting of metric linear space and normed linear space.