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In this paper, we obtain strong and ∆-convergence theorems of modified S-iteration for total asymptotically nonexpansive mappings in CAT(κ) spaces with κ > 0. Our results extend and improve the corresponding recent results announced by Panyanak [B. Panyanak, J. Inequal. Appl., 2014 (2014), 13 pages] and many authors. c ©2015 All rights reserved.

On strong and Δ -convergence of modified S-iteration for uniformly continuous total asymptotically nonexpansive mappings in CAT(κ) spaces