Iterative algorithms for finding a common fixed point of generalized nonexpansive sequences in a Hilbert space

In this research, we introduce a new general iterative method for a pair of sequences of quasi-nonexpansive mappings satisfying certain conditions and present strong convergence theorems which the iteration converge to a common fixed point of these mappings in a Hilbert space. With an appropriate setting, we obtain the corresponding results due to Aoyama and Kimura, Tain and Jin, and Wongchab and Saejung. At the end, we also apply our methods to find a common element of the set of fixed points for a sequence of quasi-nonexpansive mappings, the set of solutions of an equilibrium problem and the set of zero points for the sum of two monotone mappings.