Best coapproximation in metric linear spaces (Q2719893)

In order to obtain some characterizatons of real Hilbert spaces among real Banach spaces, a new kind of approximation, called best coapproximation, was introduced in normed linear spaces by C. Franchetti and M. Furi in 1972. Subsequently, the study was pursued in normed linear spaces and Hilbert spaces. In this paper the generalizations of some results proved earlier are obtained on the basis of the discussing of best coapproximations in metric linear spaces. The problems considered are those of existence of elements of best coapproximation and their characterization, characterizations of coproximinal, co-semi-Chebyshev and co-Chebyshev subspaces, and some properties of the best coapproximation map in metric linear spaces.