Invariant approximation for spaces

Fixed points, selections and common fixed points for nonexpansive-type mappings

“…T. Suzuki [26] proves some basic properties and gives fixed point theorems and convergence results for mappings satisfying condition (C). Following [26], A. Razani and H. Salahifard [23] state part of T. Suzuki's [26] results in the context of a complete CAT(0) space and generalize condition (C) to the multivalued case: a multivalued mapping T defined on subset of a CAT(0) space is said to satisfy condition (C) if for each x, y ∈ K and u x ∈ T (x) with (1/2)d(x, u x ) d(x, y) there exists u y ∈ T (y) such that d(u x , u y ) d(x, y). This condition is used in [23] to prove a fixed point theorem for multivalued mappings and some common fixed point results.…”

Geodesic Ptolemy spaces and fixed points

“…As remarked in [6], the following theorem proved in [15] in the setting of a complete CAT(0) space (see also [17]) holds in more general contexts. We formulate this result in the framework of geodesic Ptolemy spaces with a uniformly continuous midpoint map since the proof only requires the uniqueness of asymptotic centers and the convexity of the metric, conditions which are satisfied in such a setting.…”

Fixed point theorems for (L)-type mappings in complete CAT(0) spaces

“…For instance, in 2008, Suzuki [28] defined a class of generalized nonexpansive mappings, which he called (C)-type mappings, whose set-valued version was defined and studied in [1,2,26,30]. In 2011, García-Falset et al [14] introduced two classes of single-valued generalized nonexpansive mappings called (C λ )-type mappings and (E µ )-type mappings, respectively, which both enlarged the family of (C)-type mappings.…”