An inertially constructed forward–backward splitting algorithm in Hilbert spaces

In this paper, we develop an iterative algorithm whose architecture comprises a modified version of the forward–backward splitting algorithm and the hybrid shrinking projection algorithm. We provide theoretical results concerning weak and strong convergence of the proposed algorithm towards a common solution of the fixed point problem associated to a finite family of demicontractive operators, the split equilibrium problem and the monotone inclusion problem in Hilbert spaces. Moreover, we compute a numerical experiment to show the efficiency of the proposed algorithm. As a consequence, our results improve various existing results in the current literature.

A Shrinking Projection Algorithm with Errors for Costerro Bounded Linear Mappings

The purpose of this paper is to introduce and analyze the shrinking projection algorithm with errors for a finite set of costerro bounded linear mappings in the setting of uniformly convex smooth Banach spaces. Here, under finite dimensional or compactness restriction or the error term being zero, the strong limit point of the sequence stated in the iterative scheme for these mappings in uniformly convex smooth Banach spaces was studied. This paper extends Ezearn and Prempeh’s result for nonexpansive mappings in real Hilbert spaces.