Browder’s Convergence Theorem for Multivalued Mappings in Banach Spaces without the Endpoint Condition

We prove Browder’s convergence theorem for multivalued mappings in a uniformly convex Banach space with a uniformly Gateaux differentiable norm by using the notion of diametrically regular mappings. Our results are significant improvement on results of Jung (2007) and Panyanak and Suantai (2020)