Abstract
In this paper, a new class of nonexpansive multivalued mappings, namely, generalized $$\alpha$$ -nonexpansive multivalued mappings are introduced. Some topological properties of the fixed point sets of such mappings are derived. Existence results for common fixed points of a pair of single-valued and multivalued mappings both satisfying the generalized $$\alpha$$ -nonexpansiveness are proved. Also, weak and strong convergence results of some iterative methods are studied in a uniformly convex Banach space for approximating common fixed points of a pair of single-valued and multivalued mappings as well as two multivalued mappings satisfying the generalized $$\alpha$$ -nonexpansiveness.
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