Strong convergence theorems for total quasi-ϕ-asymptotically nonexpansive multi-valued mappings in Banach spaces

The main purpose of this article is to introduce the concept of total quasi-ϕ-asymptotically nonexpansive multi-valued mapping and prove the strong convergence theorem in a real uniformly smooth and strictly convex Banach space with Kadec-Klee property. In order to get the theorems, the hybrid algorithms are presented and are used to approximate the fixed point. The results presented in this article improve and extend some recent results announced by some authors.