ON BEST COAPPROXIMATION IN NORMED LINEAR-SPACES

This article is a brief survey of the research concerning best coapproximation, a kind of approximation introduced by C. Franchetti and M. Furi. It is concerned with the existence and uniqueness of elements of best coapproximation by elements of linear subspaces, characterizations of elements of best coapproximation, characterizations of strict convexity in terms of best coapproximation, properties of the best coapproximation operator and best coapproximation on convex sets. Some unsolved and partially solved problems raised by persons working in this field have been mentioned.