Artículo
Strongly convergent approximations to fixed points of total asymptotically nonexpansive mappings
Autor/es | Alber, Yakov
Espínola García, Rafael Lorenzo Ramírez, Josefa |
Departamento | Universidad de Sevilla. Departamento de Análisis Matemático |
Fecha de publicación | 2008-06 |
Fecha de depósito | 2016-07-22 |
Publicado en |
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Resumen | 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 ... 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. |
Cita | Alber, 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. |
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