The split common fixed point problem with families of mappings and strong convergence theorems by hybrid methods in Banach spaces. (English) Zbl 06820448

Takahashi, Wataru

Nihonkai Math. J. 27, No. 1-2, 67-88 (2016).

Summary: In this paper, we consider the split common fixed point problem with families of mappings in Banach spaces. Then using the hybrid method and the shrinking projection method, we prove strong convergence theorems for finding a solution of the split common null point problem with families of mappings in Banach spaces.

MSC:

47J25	Iterative procedures involving nonlinear operators
47H05	Monotone operators and generalizations
47H09	Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.

Keywords:

split common null point problem; fixed point; metric resolvent; hybrid method; shrinking projection method; duality mapping; strong convergence