COMMON FIXED POINTS WITH APPLICATIONS TO BEST SIMULTANEOUS APPROXIMATIONS

For a subset K of a metric space (X,d) and x ∈ X,P K (x) ={y ∈ K:d(x,y)=d(x,K) ≡ inf { d(x,k):k ∈ K }}is called the set of best K-approximant to x.An element g。 ∈ K is said to be a best simultaneous approximation of the pair y 1,y 2 ∈ X if max{d(y 1,g。),d(y 2,g。) }=inf g ∈ K max { d(y 1,g),d(y 2,g)}.In this paper,some results on the existence of common fixed points for Banach operator pairs in the framework of convex metric spaces have been proved.For self mappings T and S on K,results are proved on both T-and S-invariant points for a set of best simultaneous approximation.Some results on best K-approximant are also deduced.The results proved generalize and extend some results of I.Beg and M.Abbas 1],S.Chandok and T.D.Narang 2],T.D.Narang and S.Chandok 11],S.A.Sahab,M.S.Khan and S.Sessa 14],P.Vijayaraju 20] and P.Vijayaraju and M.Marudai 21].