Convergence of a cyclic algorithm for the split common fixed point problem without continuity assumption

Abstract

In their recent paper (Math. Model. Anal., 17(4):457–466, 2012), Tang, Peng and Liu proposed a cyclic algorithm for solving the split common fixed point problem and established its weak convergence under some certain conditions. In this paper, we shall present a simple proof of such a result and moreover we shall remove one condition, continuity of the mapping involved, ensuring the convergence of the algorithm.

Keywords

• directed mapping
• split common fixed point problem
• demicontractive mapping