ON THE PROJECTION DYNAMICAL SYSTEMS IN BANACH SPACES

Abstract

We study dynamical systems of the projection gradient type for convex constrained minimization problems, clearance type dynamical system for fixed point problems with nonexpansive self-mappings and descent-like dynamical system for variational inequalities with maximal monotone operators in Banach spaces. We prove the weak convergence of dynamical trajectories and establish the estimates of the convergence rate with respect to functionals of the problems. We also produce some strong convergence theorem. The results presented in the paper are new even in Hilbert spaces.