Generalized implicit viscosity approximation method for multivalued mappings in CAT(0) spaces

Abstract

We prove strong convergence of the sequence generated by implicit viscosity approximation method involving a multivalued nonexpansive mapping in framework of CAT(0) space. Under certain appropriate conditions on parameters, we show that such a sequence converges strongly to a fixed point of the mapping which solves a variational inequality. We also present some convergence results for the implicit viscosity approximation method in complete ℝ-trees without the endpoint condition.

Keywords

• viscosity approximation method
• variational inequality
• multivalued nonexpansive mapping
• cat(0) space
• 47j25
• 47h09
• 37c25