Abstract: We prove the following result in this paper:Let(X, J, △) be a T-complete Menger space. If {T_i, i=1, 2, …} are a sequence of the self mapping of the contractive type on X and {m_i(x), i=1, 2, …} are the functional sequence satisfying m_i(x)|m(T_i(x)), i=1, 2, …, then {T_i, i=1, 2, …} have a common fixed point.
This result is a generalization to the result obtained in I. Istratescu[7, 14]. Other results are proved concerning the fixed point theorems for G-valued metric space. The concept, the embedded theorem of S. M. space, is discussed and its relation to the existence of fixed point for above mapping is also discussed in S. M. space.