Utilizingthestabilitycharacterizationsofgeneralizedinversesoflinearoperator,weinvestigatetheexistenceofgeneralizedresolventoflinearpencilsinBanachspaces.Somepracticalcriterionsfortheexistenceofgeneralizedresolventsofthelinearpencilλ→TλSareprovidedandanexplicitexpressionofthegeneralizedresolventisalsogiven.Asapplications,thecharacterizationfortheMoore-Penroseinverseofthelinearpenciltobeitsgeneralizedresolventandtheexistenceofthegeneralizedresolventsoflinearpencilsoffiniterankoperators,Fredholmoperatorsandsemi-Fredholmoperatorsarealsoconsidered.Theresultsobtainedinthispaperextendandimprovemanyresultsinthisarea.
