Convergence and stability of iterative algorithms of generalized set-valued variational-like inclusions in Banach spaces (Q2485616)

The authors present the concept of a new proximal mapping, a natural extension of the \(P\)-proximal mapping, for a certain nonconvex lower semicontinuous subdifferentiable proper functional on a Banach space and prove its existence and Lipschitz continuity. Further, they consider a new class of generalized set-valued variational-like inclusions, which includes many known and new classes of variational (-like) inequalities (inclusions). The paper presents a development for the case of generalized set-valued variational-like inclusions for which several explicit results are known.