Theoretical Mathematics & Applications

Viscosity approximation methods for a nonexpansive multi-valued mapping in CAT(0) spaces and variational inequality

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• Abstract

  The purpose of this paper is to introduce the nonexpansive multivalued mapping in CAT(0) spaces. The convexity and closednes of a fixed point set of such mapping and demiclosed principle for such mapping are also studied. By viscosity approximation methods, We provethat the proposed implicit iteration net and sequence both converges strongly to a common fixed point of nonexpansive multi-valued mappings which is also a unique solution of the variational inequality. The results presented in the paper improve and extend various results in the current literature.