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In this paper, we consider a countable family of surjective mappings {T_n}_n N satisfying certain quasi-contractive conditions. We also construct a convergent sequence {x_n}_n N by the quasi-contractive conditions of {T_n}_n N and the boundary condition of a given complete and closed subset of a cone metric space X with convex structure, and then prove that the unique limit x^* of {x_n}_n N is the unique common fixed point of {T_n}_n N . Finally, we will give more generalized common fixed point theorem for mappings {T_i,j}_i,j N . The main theorems in this paper generalize and improve many known common fixed point theorems for a finite or countable family of mappings with quasi-contractive conditions. , number=3, journal=Analysis in Theory and Applications, year=2013, month=Jul., pages=255–266