Strong Convergence Theorems for Solutions of Equations of Hammerstein Type

Let H be a real Hilbert space. A mapping A : D(A) ⊆ H → H is said to be monotone if ⟨Ax − Ay, x − y⟩ ≥ 0 for every x, y ∈ D(A). A is called maximal monotone if it is monotone and the R(I + rA) = H, the range of (I + rA), for each r > 0, where I is the identity mapping on H. A is said to satisfy the range condition if cl(D(A)) ⊆ R(I + rA) for each r > 0. For monotone mappings, there are many related equations of evolution. Several problems that arise in differential equations, for instance, elliptic boundary value problems whose linear parts possess Green’s function, can be put in operator form as