EQUIVALENCE RELATIONS ON BEST COAPPROXIMATION AND WORST COAPPROXIMATION

A kind of approximation, called best coapproximation was introduced and discussed in normed linear spaces by C. Franchetti and M. Furi in 1972. Subsequently, this study was taken up by several researchers in different abstract spaces. In this paper, we define relations on best coapproximation and worst coapproximation. We show that these relations are equivalence relation. We obtain cosets sets of best coapproximation and worst approximation. We obtain some results on these sets, compactness and weakly compactness and define coqproximinal and coqremotal.