Generalized approximations for nonlinear three-point boundary value problems

The generalization of the method of quasilinearization for a class of second-order nonlinear nonlocal three-point boundary value problems of the types-x″=f(t,x,x′),t∈[0,1],x(0)=0,x′(1)=g(x(η)),0<η⩽1is developed. A monotone sequence of solutions of linear problems converging uniformly and rapidly to a solution of the problem is obtained in the C1 norm.