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In this paper, a new iterative scheme for a finite family of \(I_{i}\)-generalized asymptotically nonexpansive nonself-mappings \(\{T_{i}\} _{i=1}^{r}\) is constructed in a uniformly convex hyperbolic space. We establish strong convergence theorems of this iterative scheme to a common fixed point of \(\{T_{i}\}_{i=1}^{r}\) and \(\{ I_{i}\}_{i=1}^{r}\) under certain conditions. Our results of this paper extend some results in the literature.

Convergence of general algorithm for I-generalized asymptotically nonexpansive nonself-mappings in uniformly convex hyperbolic spaces