A new iterative scheme for finding attractive points of (α, β)-generalized hybrid set-valued mappings

In this paper, we first introduce the notions of (α, β)-generalized hybrid set-valued mappings, strongly attractive points, attractive points and condition I . Then we construct an iterative method for finding attractive points of (α, β)-generalized hybrid set-valued mappings and obtain some convergence theorems of the proposed iterative scheme for (α, β)-generalized hybrid set-valued mappings defined on a uniformly convex Banach space by using of condition I! and demi-compact property, respectively.