In this paper, we introduce a new iterative method for nonexpansive mappings in CAT(\kappa) spaces. First, the rate of convergence of proposed method and comparison with recently existing method is proved. Second, strong and \Delta-convergence theorems of the proposed method in such spaces under some mild conditions are also proved. Finally, we provide some non-trivial examples to show efficiency and comparison with many previously existing methods.

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  Pakkaranang, Nuttapol,   Uddin, Izhar,  Bantaojai, Thanatporn,  Yimmuang,  Panu, Garodia, Chanchal