Projection methods for quasi-nonexpansive multivalued mappings in Hilbert spaces

Abstract

This paper proposes a modified D-iteration to approximate the solutions of three quasi-nonexpansive multivalued mappings in a real Hilbert space. Due to the incorporation of an inertial step in the iteration, the sequence generated by the modified method converges faster to the common fixed point of the mappings. Furthermore, the generated sequence strongly converges to the required solution using a shrinking technique. Numerical results obtained indicate that the proposed iteration is computationally efficient and outperforms the standard forward-backward with inertial step.

Keywords

• quasi-nonexpansive multivalued mappings
• weak and strong convergence
• inertial technical term
• d-iteration
• projection methods