Strong and weak convergence theorems for solutions of equations of Hammerstein-type

In this paper, it is our aim in this paper to introduce a new iterative algorithm for approximation of a solution of an equation of Hammerstein-type. The proposed scheme does not involve computation of inverse of operators under study; it does not involve passing through computation of a certain set that must contain a solution of the equation of Hammerstein-type before convergence takes place. The proposed scheme requires only one parameter satisfying verifiable mild conditions. Moreover, the mappings involved are neither defined on compact subset of the space under study, nor assumed to be angle bounded. Our theorems complement several results that have been obtained in this direction.