Artículos (Análisis Matemático)

URI permanente para esta colecciónhttps://hdl.handle.net/11441/10809

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Strongly convergent approximations to fixed points of total asymptotically nonexpansive mappings
(Springer, 2008-06) Alber, Yakov; Espínola García, Rafael; Lorenzo Ramírez, Josefa; Universidad de Sevilla. Departamento de Análisis Matemático; Universidad de Sevilla. FQM127: Análisis Funcional no Lineal
In 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.