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In this paper, we construct an inertial algorithm that approximates a common fixed point of a countable family of multi-valued total asymptotically strict quasi-$\phi$-pseudocontractive maps in real Banach spaces and prove strong convergence of the sequence generated by this algorithm. We provide a numerical example to illustrate the implementability of the proposed algorithm and also show that our algorithm converges faster than some algorithms recently proposed by other authors for solving this class of problem. Furthermore, we present some applications of our theorems. Finally, our theorems are significant improvement on several important recent results.

Strong convergence theorems of an inertial algorithm for approximating common fixed points of a family of multi-valued pseudocontractive-type maps