Convergence results on the general inertial Mann–Halpern and general inertial Mann algorithms

Abstract

Abstract In this paper, we prove strong convergence theorem of the general inertial Mann–Halpern algorithm for nonexpansive mappings in the setting of Hilbert spaces. We also prove weak convergence theorem of the general inertial Mann algorithm for k-strict pseudo-contractive mappings in the setting of Hilbert spaces. These convergence results extend and generalize some existing results in the literature. Finally, we provide examples to verify our main results.

Keywords

• Mann algorithm
• Inertia
• Halpern algorithm
• Nonexpansive mapping
• k-strict pseudo-contractive mapping