Algorithms for Hammerstein inclusions in certain Banach spaces
Moustapha Sène, Mariama Ndiaye, Ngalla Djitté · The Journal of Nonlinear Sciences and Applications · 2019
Let \(E\) be a reflexive smooth and strictly convex real Banach space. Let \(F: E\rightarrow 2^{E^*}\) and \(K: E^*\rightarrow E\) be bounded maximal monotone mappings such that \(D(F)=E\) and \(R(F)=D(K)=E^*\). Suppose that the Hammerstein inclusion \(0\in u+KFu \) has a solution in \(E\). We present in this paper a new algorithm for approximating solutions of the inclusion \(0\in u+KFu \). Then we prove strong convergence theorems. Our theorems improve and unify most of the results that have been proved in this direction for this important class of nonlinear mappings. Furthermore, our technique of proof is of independent interest.