Viscosity Iteration in CAT(κ) Spaces

Abstract

We study the approximation of fixed points of nonexpansive mappings in CAT(κ) spaces. We show that the iterative sequence generated by the Moudafi's viscosity type algorithm converges to one of the fixed points of the nonexpansive mapping depending on the contraction applied in the algorithm.

Keywords:

• CAT(κ) spaces
• Fixed points
• Nonexpansive mappings
• Viscosity iterates

Mathematics Subject Classification:

• Primary 47H09
• Secondary 47H10, 53C22