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In the present note we are concerned with the question of the existence and uniqueness of solutions of two-point boundary value problem for nonlinear difference equations with parameters in Banach space.The proof of the above problem is based on the method of successive approximation and fixed-point method. 2000 Mathematics Subject Classification. 39A10, 47H10.doi:10.3336/gm.38.2.09 fatcat:ouhcd7dja5f3re3fewehvjitoe