The modified S-iteration process for nonexpansive mappings in CAT(κ)$\operatorname{CAT}(\kappa)$ spaces

We denote the set of all fixed points of T by Fix(T); for more details see []. The concept of -convergence in general metric spaces was introduced by Lim []. Kirk [] has proved the existence of fixed point of nonexpansive mappings in CAT() spaces. Kirk and Panyanak [] specialized this concept to CAT() spaces and showed that many Banach space results involving weak convergence have precise analogs in this setting. Dhompongsa and Panyanak [] continued to work in this direction. Their results involved theMann and Ishikawa iteration process involving onemapping. After that Khan and Abbas [] studied the approximation of common fixed point by the Ishikawa-type iteration process involving two mappings in CAT() spaces. The Mann iteration process [] was defined by x ∈ C and xn+ = anTxn ⊕ ( – an)xn, n≥ , (.)