Common Attractive Points of Generalized Hybrid Multi-Valued Mappings and Applications - Lili Chen; Ni Yang; Jing Zhou (Mathematics, 2020)
In this paper, we first propose the concepts of <semantics>(ζ,η,λ,π)</semantics>-generalized hybrid multi-valued mappings, the set of all the common attractive points (<semantics>CAf,g</semantics>) and the set of all the common strongly attractive points (<semantics>CsAf,g</semantics>), respectively for the multi-valued mappings f and g in a CAT(0) space. Moreover, we give some elementary properties in regard to the sets <semantics>Af</semantics>, <semantics>Ff</semantics> and <semantics>CAf,g</semantics> for the multi-valued mappings f and g in a complete CAT(0) space. Furthermore, we present a weak convergence theorem of common attractive points for two <semantics>(ζ,η,λ,π)</semantics>-generalized hybrid multi-valued mappings in the above space by virtue of Banach limits technique and Ishikawa iteration respectively. Finally, we prove strong convergence of a new viscosity approximation method for two <semantics>(ζ,η,λ,π)</semantics>-generalized hybrid multi-valued mappings in CAT(0) spaces, which also solves a kind of variational inequality problem.