Strongly convergent approximations to fixed points of total asymptotically nonexpansive mappings期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Strongly convergent approximations to fixed points of total asymptotically nonexpansive mappings

Authors:

Institution:

(1) Department of Mathematics, The Technion-Israel Institute of Technology, 32000 Haifa, Israel;(2) Departamento de Análisis Matemático, Universidad de Sevilla, P. O. Box 1160, 41080 Seville, Spain

Abstract:

In this work we prove a new strong convergence result of the regularized successive approximation method given by

$y_{n + 1} = q_n z_0 + (1 - q_n )T^n y_n , n = 1,2, \ldots ,$

where

$\mathop {\lim }\limits_{n \to \infty } q_n = 0 and \sum\limits_{n = 1}^\infty {q_n = \infty ,}$

for T a total asymptotically nonexpansive mapping, i.e., T is such that

$\left\| {T^n x - T^n y} \right\| \leqslant \left\| {x - y} \right\| + k_n^{(1)} \varphi (\left\| {x - y} \right\|) + k_n^{(2)} ,$

where k _n¹ and k _n² are real null convergent sequences and ϕ: R ⁺ → R ⁺ is continuous such that ϕ(0) = 0 and lim_t→∞ 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. The second and third authors are partially supported by the Ministry of Science and Technology of Spain, Grant BFM 2000-0344-CO2-01 and La Junta de Antalucía Project FQM-127

Keywords:

asymptotically nonexpansive mappings best approximation fixed point duality map iteration schemes

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