Zuo, Zhanfei; Huang, Yi; Chen, Xiaochun; Chen, Feixiang; Tu, Zhengwen \(\Delta\)-convergence theorem for total asymptotically nonexpansive mapping in uniformly convex hyperbolic spaces. (English) Zbl 1330.47091 Ital. J. Pure Appl. Math. 33, 401-410 (2014). Summary: Recently, S. S. Chang et al. [Appl. Math. Comput. 219, No. 5, 2611–2617 (2012; Zbl 1308.47060)] introduced the concept of total asymptotically nonexpansive mappings which contain the asymptotically nonexpansive mappings. The purpose of the present paper is to analyze a three-step iterative scheme for total asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces. Meanwhile, we obtain a \(\Delta\)-convergence theorem of the three-step iterative scheme for total asymptotically nonexpansive mapping in CAT\((0)\) spaces. Our results obtained in this paper extend and improve some previously known results. MSC: 47J25 Iterative procedures involving nonlinear operators 47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. 54H25 Fixed-point and coincidence theorems (topological aspects) Keywords:total asymptotically nonexpansive mapping; three-step iterations; uniformly convex hyperbolic spaces; \(\Delta\)-convergence theorem; CAT\((0)\) spaces Citations:Zbl 1308.47060 PDFBibTeX XMLCite \textit{Z. Zuo} et al., Ital. J. Pure Appl. Math. 33, 401--410 (2014; Zbl 1330.47091) Full Text: Link