Let H be a real Hilbert spae and F; K : H ! H be mappings such that DðKÞ ¼ DðFÞ ¼ H. Suppose that... more Let H be a real Hilbert spae and F; K : H ! H be mappings such that DðKÞ ¼ DðFÞ ¼ H. Suppose that Hammerstein equation of the type u þ KFu ¼ 0 has a solution in H, then we studied in this paper methods that contain an auxiliary mapping (defined on an appropriate real Hilbert space in terms of the mappings K and F) which is pseudocontractive whenever K and F are monotone; and approximation of a fixed point of this pseudocontractive mapping induces approximation of a solution of the equation u þ KFu ¼ 0. Moreover, the mappings K and F need not be defined on compact subset of H or angle bounded on H. Furthermore, our methods which do not involve K À1 provide an implicit algorithm for approximation of solutions of the equation u þ KFu ¼ 0 whenever K and F are assumed to be bounded and continuous; if K and F are assumed to be Lipschitz continuous, then an explicit iterative algorithm for computation of solutions of the equation u þ KFu ¼ 0 is provided, still without involving K À1 .
Let H be a real Hilbert spae and F; K : H ! H be mappings such that DðKÞ ¼ DðFÞ ¼ H. Suppose that... more Let H be a real Hilbert spae and F; K : H ! H be mappings such that DðKÞ ¼ DðFÞ ¼ H. Suppose that Hammerstein equation of the type u þ KFu ¼ 0 has a solution in H, then we studied in this paper methods that contain an auxiliary mapping (defined on an appropriate real Hilbert space in terms of the mappings K and F) which is pseudocontractive whenever K and F are monotone; and approximation of a fixed point of this pseudocontractive mapping induces approximation of a solution of the equation u þ KFu ¼ 0. Moreover, the mappings K and F need not be defined on compact subset of H or angle bounded on H. Furthermore, our methods which do not involve K À1 provide an implicit algorithm for approximation of solutions of the equation u þ KFu ¼ 0 whenever K and F are assumed to be bounded and continuous; if K and F are assumed to be Lipschitz continuous, then an explicit iterative algorithm for computation of solutions of the equation u þ KFu ¼ 0 is provided, still without involving K À1 .
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