Diametrically Regular Mappings and Browder’s Theorem Without the Endpoint Condition

Abstract

© 2019, © 2019 Taylor & Francis Group, LLC. In this paper, we introduce the class of diametrically regular mappings and prove that it includes the class of multi-valued mappings having endpoints. We also prove the existence of endpoints and the convergence of an iterative process for mappings of this class. Our approach provides a new idea of proving Browder’s theorem without the endpoint condition.