Inertial Krasnoselski–Mann Iterative Method for Solving Hierarchical Fixed Point and Split Monotone Variational Inclusion Problems with Its Applications

Abstract

In this article, we discuss the hierarchical fixed point and split monotone variational inclusion problems and propose a new iterative method with the inertial terms involving a step size to avoid the difficulty of calculating the operator norm in real Hilbert spaces. A strong convergence theorem of the proposed method is established under some suitable control conditions. Furthermore, the proposed method is modified and used to derive a scheme for solving the split problems. Finally, we compare and demonstrate the efficiency and applicability of our schemes for numerical experiments as well as an example in the field of image restoration.

Keywords

• variational inclusion problem
• inertial technique
• strong convergence
• image restoration
• hierarchical fixed point problem