Recently M. Stieglitz introduced the concept of Fg -convergence of sequcnce and generalized the results of Eizen and Laush, King, and Shaefer for more general classes of matrices. Quite recently Ahmad and Mursaleen have extended the space Fg of Fg - convergent sequences to Fg (p). In the present paper we furnished a sel of ne- cessary and sufficient conditions for each (co (p), Fo g (p)), (1 (p), Fg ) and (Mo (p), Fg ) matrices.