ON l -FIRMLY NONEXPANSIVE MAPPINGS IN UNIQUE GEODESIC SPACES
David Ariza‐Ruiz · 2011
In 1922 Stefan Banach published the well-known Contraction Mapping Principle. With this result, a new branch of Mathematical Analysis appeared: Metric Fixed Point Theory as we know it nowadays. The interest in this theory reemerged in 1965 when, simultaneously but independently, W.A. Kirk [7], F. Browder [2, 3] and Gohde [6] proved the existence of fixed points in Banach spaces for nonexpansive mappings, which represent a more general class of mappings than that of contraction mappings. In 1967 Browder [4] defined a new subclass of nonexpansive mappings on Hilbert spaces. These mappings are commonly called λ-firmly nonexpansive mappings, with 0 ≤ λ < 1. Six years later, Bruck [5] studied this class of mappings on a general normed space.