The split common fixed point problem for infinite families of total quasi-asymptotically nonexpansive operators (Q466851)

In this paper, a new iterative approximation method is introduced. Lemma 2.1 is the key result which sets the stage for the proof of their two main theorems. This type of lemmas are an essential part of strong convergence results via fixed point theory. In their first main theorem (Theorem 2.2), using this iterative method, a strong convergence theorem for an infinite family of total quasi-asymptotically nonexpansive operators is proved. In their second main theorem (Theorem 2.4), a weak convergence theorem is proved. A couple of examples are given to support the results. Example 2.3 tells how the iterative approximation method is implemented, whereas Example 2.5 illustrates its effectiveness for infinite families of total quasi-asymptotically nonexpansive operators on the real line taken as a Hilbert space.