Common fixed points by a generalized iteration scheme with errors

Abstract

In this paper, we introduce a generalized iteration scheme with errors for convergence to common fixed points of two nonexpansive mappings. This scheme contains a wide variety of existing iteration schemes as its special cases. The main feature of this scheme is that its special cases can handle both strong convergence like Halpern-type and weak convergence like Ishikawa-type iteration schemes. Our main theorem will in particular generalize a recent result by Kim and Xu [9]

Keywords

• Generalized iteration scheme
• Common fixed point
• Nonexpansive mapping
• Weak convergence