Strong and Δ-Convergence Theorems for Common Fixed Points of a Finite Family of Multivalued Demicontractive Mappings in CAT(0) Spaces

Abstract

Let K be a nonempty closed and convex subset of a complete CAT(0) space. Let $T_i:K\to \text{C}\text{B}\left(K\right),i=\mathrm{1,2},\dots ,m$, be a family of multivalued demicontractive mappings such that $F:={\bigcap }_{i=1}^{m}F(T_i)\ne \varnothing$. A Krasnoselskii-type iterative sequence is shown to $\Delta$-converge to a common fixed point of the family $\left\{T_i,i=\mathrm{1,2},\dots ,m\right\}$. Strong convergence theorems are also proved under some additional conditions. Our theorems complement and extend several recent important results on approximation of fixed points of certain nonlinear mappings in CAT$(\mathrm{0})$ spaces. Furthermore, our method of the proof is of special interest.