On Continuity of Browder Type Fixed Points

To study the stability of Browder type fixed points, two kinds of usual metrics for set-valued mappings are discussed. Noting that the set of fixed points for a Browder type set-valued mapping may be noncompact, a metric is introduced to construct a complete metric space on a kind of these mappings. Some results for continuity of Browder type fixed points are obtained, and we prove that each fixed point for each Browder type set-valued mapping is essentially stable.