Common fixed points of quasi-nonexpansive sequences in Hadamard spaces

In this paper, we prove that the common fixed point set of a given quasi-nonexpansive sequence is identical to the fixed point set of a single quasi-nonexpansive mapping. We also generalize the concept of balanced mappings in Termkaew et al. ’s paper (Open Math. 21 (2023)), which was introduced and studied by Hasegawa and Kimura (Linear Nonlinear Anal. 4 (2018)), from a sequence of nonexpansive mappings to a quasi-nonexpansive sequence and investigate its fundamental properties. Furthermore, we can use balanced mapping to prove the above result for a quasi-nonexpansive sequence, and we establish the necessary and sufficient condition to conclude that balanced mapping is a Δ-demiclosed mapping. Moreover, we propose and study one of the convex combinations inspired by Kimura et al. (Fixed Point Theory Appl. 2013:336 (2013)) and obtain the same results as for balanced mappings.