Cascading Operators in CAT(0) Spaces

Abstract

In this work, we introduce the notion of cascading non-expansive mappings in the setting of CAT(0) spaces. This family of mappings properly contains the non-expansive maps, but it differs from other generalizations of this class of maps. Considering the concept of Δ-convergence in metric spaces, we prove a principle of demiclosedness for this type of mappings and a Δ-convergence theorem for a Mann iteration process defined using cascading operators.

Keywords

• cascading non-expansive mappings
• CAT(0) space
• fixed point property
• Mann iteration