ForasubsetKofametricspace(X,d)andx∈X,PK(x)={y∈K:d(x,y)=d(x,K)≡inf{d(x,k):k∈K}}iscalledthesetofbestK-approximanttox.Anelementg。∈Kissaidtobeabestsimultaneousapproximationofthepairy1,y2∈Xifmax{d(y1,g。),d(y2,g。)}=infg∈Kmax{d(y1,g),d(y2,g)}.Inthispaper,someresultsontheexistenceofcommonfixedpointsforBanachoperatorpairsintheframeworkofconvexmetricspaceshavebeenproved.ForselfmappingsTandSonK,resultsareprovedonbothT-andS-invariantpointsforasetofbestsimultaneousapproximation.SomeresultsonbestK-approximantarealsodeduced.TheresultsprovedgeneralizeandextendsomeresultsofI.BegandM.Abbas[1],S.ChandokandT.D.Narang[2],T.D.NarangandS.Chandok[11],S.A.Sahab,M.S.KhanandS.Sessa[14],P.Vijayaraju[20]andP.VijayarajuandM.Marudai[21].
