The iterative solutions of split common fixed point problem for asymptotically nonexpansive mappings in Banach spaces

Abstract

Abstract In this paper, we propose an iteration algorithm for finding a split common fixed point of an asymptotically nonexpansive mapping in the frameworks of two real Banach spaces. Under some suitable conditions imposed on the sequences of parameters, some strong convergence theorems are proved, which also solve some variational inequalities that are closely related to optimization problems. The results here generalize and improve the main results of other authors.

Keywords

• Split common fixed point
• Strong convergence
• Variational inequality
• Asymptotically nonexpansive mapping