BEST COAPPROXIMATION IN METRIC LINEAR SPACES

Abstract


 
 
 In order to obtain some characterizations 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 [3] in 1972. Subsequently, the study was pursued in normed linear spaces and Hilbert spaces by H. Berens, L. Hetzelt, T. D. Narang, P. L. Papini, Gectha S. Rao and her students, Ivan Singer and a few others (see, e.g., [1], [4], [7], [9], [13 to 15], and [17 to 20]). In this paper, we discuss best coapproximation in metric linear spaces thereby generalizing some of the results proved in [3], [7], [13], and [18]. The problems considered are those of existence of elements of best coapproximation and their characterization, characteriza­ tions of coproximinal, co-semi-Chebyshev and co-Chebyshev subspaces, and some properties of the best coapproximation map in metric linears space.