An inertial S-iteration process

Abstract

Abstract In this paper, we establish a new iteration method, called an InerSP (an inertial S-iteration process), by combining a modified S-iteration process with the inertial extrapolation. This strategy is for speeding up the convergence of the algorithm. We then prove the convergence theorems of a sequence generated by our new method for finding a common fixed point of nonexpansive mappings in a Banach space. We also present numerical examples to illustrate that the acceleration of our algorithm is effective.

Keywords

• Common fixed point
• MIS-iteration
• Nonexpansive mapping
• Inertial extrapolation