A simple computational algorithm with inertial extrapolation for generalized split common fixed point problems

Abstract

In the present paper, we explore operator norm independent inertial type accelerated iterative algorithm solving generalized split common fixed point problem, which is the problem of finding a point that belongs to the intersection of a finite family of fixed point sets of demimetric mappings such that its image under a finite number of linear transformations belongs to the intersection of another finite family of fixed point sets of demimetric mappings in the image space. We adopt rules for selecting the step size such that the implementation of our proposed algorithm does not need any prior information about the operator norms. The strong convergence result is analyzed and some applications of our proposed algorithm are demonstrated. Our result in this paper will improve and generalize many results in the literature. Numerical experiments show that our iteration method is very effective for approximating the solution point of problem under consideration.

Keywords

• Split common fixed-point problem
• κ-demimetric mapping
• Inertial method
• Strong convergence
• Hilbert space