In this paper, we prove some fixed point properties and demiclosedness principle for multivalued generalized 𝛼-nonexpansive mappings in uniformly convex hyperbolic spaces. We also proposed a three steps iterative scheme for approximating the common fixed points of generalized 𝛼-nonexpansive mapping and prove some strong and Δ-convergence theorems for such operator in the setting of uniformly convex hyperbolic space. We provide a numerical example to show that the three steps scheme proposed in this paper performs better than the modified SP-iterative scheme. The results obtained in this paper extend and generalized the corresponding results in uniformly convex Banach spaces, CAT(0) space and many other results in this direction.
Keywords: Generalized nonexpansive, three steps iteration, multivalued mappings, hyperbolic spaces, fixed point theorems.