Abstract
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 ⩽ 1 is developed. A monotone sequence of solutions of linear problems converging uniformly and rapidly to a solution of the problem is obtained in the C 1 norm.
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