Fixed points of set-valued mappings satisfying a Banach orbital condition

Abstract

In this note, we prove a fixed point existence theorem for set-valued functions by extending the usual Banach orbital condition concept for single valued mappings. As we show, this result applies to various types of set-valued contractions existing in the literature.

Keywords

• banach orbital condition
• continuity of set-valued mappings
• fixed point
• hausdorff upper semicontinuity
• set-valued contraction