THE SPLIT COMMON FIXED POINT PROBLEM FOR TWO INFINITE FAMILIES OF NONLINEAR MAPPINGS IN HILBERT SPACES

摘要

In this paper, we deal with the split common fixed point problem for two infinite families of demigeneric generalized hybrid mappings and generic generalized hybrid mappings in Hilbert spaces. The class of demigeneric generalized hybrid mappings covers strict pseudo-contractions defined by Browder and Petryshyn [6] and generalized hybrid mappings defined by Kocourek, Takahashi and Yao [18] and the class of generic generalized hybrid mappings covers nonexpansive mappings, nonspreading mappings and hybrid mappings in Hilbert spaces. We first obtain a crucial lemma for the proof of our main theorem which is related to an infinite sum of quasi-nonexpansive mappings and then prove a strong convergence theorem of Halpern's type [13] for finding a solution of the split common fixed point problem for two infinite families of demigeneric generalized hybrid mappings and generic generalized hybrid mappings in Hilbert spaces. Using this result, we obtain new strong convergence theorems which are related to the split common fixed point problem in Hilbert spaces.