WeprovideconvergenceresultsanderrorestimatesforNewton-likemethodsingeneralizedBanachspaces.TheideaofageneralizednormisusedwhichisdefinedtobeamapfromalinearspaceintoapartiallyorderedBanachspace.Convergenceresultsanderrorestimatesareimprovedcomparedwiththerealnormtheory.