A spherically vicinal mapping on geodesic spaces with curvature bounded above

Takuto Kajimura, Yasunori Kimura

Abstract

In 2018, vicinal mappings and firmly vicinal mappings were proposed by Kohsaka. He showed fundamental properties of firmly vicinal mappings and a fixed point theorem for those mappings. In this paper, we propose spherically vicinal mappings and firmly spherically vicinal mappings whose classes contain those of vicinal mappings and firmly vicinal mappings, respectively. We also show some examples of its mapping and prove fundamental properties and an approximation theorem to a fixed point.