Fixed point theorems and convergence theorems for some generalized nonexpansive mappings

Abstract

We introduce some condition on mappings. The condition is weaker than nonexpansiveness and stronger than quasinonexpansiveness. We present fixed point theorems and convergence theorems for mappings satisfying the condition.

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.…”

Strong and weak convergence of an iterative process for a finite family of multivalued mappings satisfying the condition (C)

“…In 2008, Suzuki [17] introduced a condition on mappings, called (C) which is weaker than nonexpansiveness and stronger than quasi-nonexpansiveness. A multivalued mapping T : E !…”

Metric fixed point theory on hyperconvex spaces: recent progress

“…The nonexpansiveness condition (C), also known as Suzuki condition, was introduced in [65] to study mild nonexpansiveness conditions which still imply existence of fixed points.…”