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

The main purpose in this paper is to introduce an original technique, namely, a specific way of choosing the indexes of the involved operators, by which a new iterative algorithm is developed for solving the split common fixed point problem for infinite families of total quasi-asymptotically nonexpansive operators and some strong and weak convergence theorems are established for this class of nonlinear operators in the framework of infinite-dimensional Hilbert spaces. The result is more applicable than those of other authors with related interest.