Strong convergence theorem for quasi-ϕ-asymptotically nonexpansive mappings in the intermediate sense in Banach spaces

In this paper, we modify Halpern and Mann’s iterations for finding a fixed point of an infinite family of quasi-ϕ-asymptotically nonexpansive mappings in the intermediate sense in Banach spaces. We prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm in a uniformly smooth and strictly convex Banach space which also enjoys the Kadec-Klee property. The results presented in this paper improve and extend some recent corresponding results.