Thispaperdiscussespointwiseerrorestimatesfortheapproximationbyboundedlinearoperatorsofcontinuousfunctionsdefinedoncompactmetricspaces(X,d),Theauthorsintroduceanewmajorautofthemodulusofthecontinuitywhichisthesrnallestamongthoseg(ξ)'swhichhavethefollowingpropertiesω(f，ε)≤9(f，ε)andg(f,λε)≤(1+λ)g(f,ε)andbythismajorantanewquantitativeKorovkintypetheoremonanycompactmetricspaceisproved.
