In the present work our intention is to establish relationship between new types of closed sets namely g*b-closed sets (resp.gb-closed) and g*i-closed sets(resp.gi-closed) and g*b-closed sets(resp.gb-closed) and g*d-closed sets(resp.gd-closed). We also established the independency between the notions g*i-closedness (resp.gi-closedness) and g*d-closedness (resp.gd-closedness).