In this paper, it is discussed by using cone and upper and lower solutions mono- tone iterative theory of mixed monotone operator that the bounary value problem is more generalized style to system of equations in the form of -u = f(t, u, v) -v = g(t, u, v) u(0) = u(1) = 0 v(0) = v(1) = 0 in abstract space. Moreover, it is obtained unique solutions for system of equations and error estimations between approximation iteration sequence and exact solution under more simpler conditions. Therefore, some new results which extend and improve the related known works in the literatures are obtained.
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