on generalized φ-strongly monotone mappings and algorithms for the solution of equations of hammerstein type

In this paper, we consider the class of generalized φ-strongly monotone mappings and the methods of approximating a solution of equations of hammerstein type. auxiliary mapping is defined for nonlinear integral equations of hammerstein type. the auxiliary mapping is the composition of bounded generalized φ-strongly monotone mappings which satisfy the range condition. suitable conditions are imposed to obtain the boundedness and to show that the auxiliary mapping is a generalized φ-strongly which satisfies the range condition. a sequence is constructed and it is shown that it converges strongly to a solution of equations of hammerstein type. the results in this paper improve and extend some recent corresponding results on the approximation of a solution of equations of hammerstein type.