Iterative Methods for the Sum of Two Monotone Operators

The set of solutions of 1.1 is denoted by A B −1 0 . A number of problems arising in structural analysis, mechanics, and economics can be studied in the framework of this kind of variational inclusions; see, for instance, 1–4 . The problem 1.1 includes many problems as special cases. 1 If B ∂φ : H → 2 , where φ : H → R ∪ ∞ is a proper convex lower semicontinuous function and ∂φ is the subdif and if onlyerential of φ, then the variational inclusion problem 1.1 is equivalent to find u ∈ H such that 〈 Au, y − u φy − φ u ≥ 0, ∀y ∈ H, 1.2