Fixed points of continuous pseudocontractive mappings on convex, closed unbounded domains
Jesús Garcı́a-Falset · Proceedings of the American Mathematical Society · 2024
The purpose in this article is to discuss under what conditions a continuous pseudocontractive mapping, in particular a nonexpansive map, has a fixed point when its domain is a closed, convex and unbounded subset of a Banach space. In fact, we will give a characterization of this property. The Halpern iterative algorithm for nonexpansive mappings is also investigated.