Convergence rate analysis for averaged fixed point iterations in the presence of H\"older regularity

摘要: In this paper, we establish sublinear and linear convergence of fixed point iterations generated by averaged operators in a Hilbert space. Our results are achieved under bounded H older regularity assumption which generalizes the well-known notion regularity. As an application our results, provide rate analysis for Krasnoselskii– Mann iterations, cyclic projection algorithm, Douglas–Rachford feasibility algorithm along with some variants. important case underlying sets convex described polynomials finite dimensional space, show that properties automatically satisfied, from follows.