  In the paper, we introduce several accelerate iterative algorithms for
solving the multiple-set split common fixed-point problem of quasi-nonexpansive
operators in real Hilbert space. Based on primal-dual method, we construct
several iterative algorithms in a way that combines inertial technology and the
self-adaptive stepsize such that the implementation of the algorithms doesn't
need any prior information about bounded linear operator norm. Under suitable
assumptions, weak convergence of the proposed algorithms is established. As
applications, we obtain relative iterative algorithms to solve the multiple-set
split feasibility problem. Finally, the performance of the proposed algorithms
is illustrated by numerical experiments.
