Strong Convergence of Modified Inertial Mann Algorithms for Nonexpansive Mappings

Abstract

In this paper, we introduce two new modified inertial Mann Halpern and viscosity algorithms for solving fixed point problems. We establish strong convergence theorems under some suitable conditions. Finally, our algorithms are applied to split feasibility problem, convex feasibility problem and location theory. The algorithms and results presented in this paper can summarize and improve corresponding results previously known in this area.

Strong convergence of inertial Mann algorithms for solving hierarchical fixed point problems

“…In particular, an inertial type extrapolation was first proposed by Polyak [14] as an acceleration process. In recent years, some authors constructed various fast iterative algorithms with the aid of inertial extrapolation techniques, such as, inertial Mann algorithms [19], inertial forward-backward splitting algorithms [17], inertial extragradient algorithms [9], inertial gradient algorithms [18], inertial projection algorithms [10,21] and fast iterative shrinkage-thresholding algorithm (FISTA) [3].…”

Self adaptive inertial extragradient algorithms for solving variational inequality problems

“…On the other hand, in recent years, there has been tremendous interest in developing fast iterative algorithms. Many authors have used inertial methods to devise a large number of iterative algorithms that can improve the convergence speed; see, for example, [17,18,19,20,21,22,23] and the references therein.…”

Strong convergence of two inertial projection algorithms in Hilbert spaces

“…These algorithms have shown advantages in theory and numerical experiments, and have been applied to fields such as image processing and machine learning. For more discussion, we recommend readers to refer to [1,3,6,11,12,22] and the references therein.…”