Abstract
In this paper, we introduce a new iterative procedure which is constructed by the shrinking hybrid projection method for solving the common solution of fixed point problems for two total quasi-ϕ-asymptotically nonexpansive multi-valued mappings. Under suitable conditions, the strong convergence theorems are established in a uniformly smooth and strictly convex real Banach space with Kadec-Klee property. Our result improves and extends the corresponding ones announced by some authors.
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