Alber, YakovEspínola García, RafaelLorenzo Ramírez, Josefa2016-07-222016-07-222008-06Alber, Y., Espínola García, R. y Lorenzo Ramírez, J. (2008). Strongly convergent approximations to fixed points of total asymptotically nonexpansive mappings. Acta Mathematica Sinica, English Series, 24 (6), 1005-1022.1439-85161439-7617http://hdl.handle.net/11441/43918In this work we prove a new strong convergence result of the regularized successive approximation method given by yn+1 = qnz0 + (1 − qn)T n yn, n = 1, 2, ..., where limn→∞ qn = 0 and X∞ n=1 qn = ∞, for T a total asymptotically nonexpansive mapping, i.e., T is such that kT nx − T n yk ≤ kx − yk + k (1) n φ(kx − yk) + k (2) n , where k 1 n and k 2 n are real null convergent sequences and φ : R+ → R+ is continuous and such that φ(0) = 0 and limt→∞ φ(t) t ≤ C for a certain constant C > 0. Among other features, our results essentially generalize existing results on strong convergence for T nonexpansive and asymptotically nonexpansive. The convergence and stability analysis is given for both self- and nonself-mappings.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Asymptotically nonexpansive mappingsBest approximationFixed pointduality mapIteration schemesinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1007/s10114-007-6367-6