Averaged Iterative Algorithms for Convex Optimization Problems over a Common Fixed-Points Set of Demicontractive Mappings

In this article, we introduce a novel averaged-type iterative scheme designed for solving convex minimization problems over the set of common fixed points of a pair of demicontractive mappings. Under suitable assumptions, we prove that the proposed algorithm converges strongly to the solution of the considered problem in a Hilbert space setting. We further demonstrate the applicability of our method to quadratic optimization problems with a bounded linear operator. In addition, we also report the numerical experiments that were performed in order to demonstrate the convergence behavior of the algorithm and to highlight its superiority over related existing methods.