Strongly Convergent Approximations to Fixed Points of Total Asymptotically Nonexpansive Mappings  

作　　者：Yakov ALBER Rafa ESPíNOLA Pepa LORENZO 

机构地区：[1]Department of Mathematics,The Technion-Israel Institute of Technology,32000 Haifa,Israel [2]Departamento de Andlisis Matemdtico,Universidad de Sevilla,P.O.Box 1160,41080-Seville,Spain

出　　处：《Acta Mathematica Sinica,English Series》2008年第6期1005-1022,共18页数学学报（英文版）

基　　金：the Ministry of Science and Technology of Spain,Grant BFM 2000-0344-CO2-01;La Junta de Antalucia Project FQM-127

摘　　要：In this work we prove a new strong convergence result of the regularized successive approximation method given by yn＋1 = qnz0 ＋ （1 - qn）T^nyn, n = 1, 2,…,where lim n→∞ qn = 0 and ∞∑n=1 qn=∞ for T a total asymptotically nonexpansive mapping, i.e., T is such that ││T^n x - T^n y││ ≤ x - y ││ ＋ kn^（1）φ（││x - y││） ＋ kn^（2）,where kn^1 and kn^2 are real null convergent sequences and φ：R^＋→R^＋ is continuous 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.In this work we prove a new strong convergence result of the regularized successive approximation method given by yn＋1 = qnz0 ＋ （1 - qn）T^nyn, n = 1, 2,…,where lim n→∞ qn = 0 and ∞∑n=1 qn=∞ for T a total asymptotically nonexpansive mapping, i.e., T is such that ││T^n x - T^n y││ ≤ x - y ││ ＋ kn^（1）φ（││x - y││） ＋ kn^（2）,where kn^1 and kn^2 are real null convergent sequences and φ：R^＋→R^＋ is continuous 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.

关 键 词：asymptotically nonexpansive mappings best approximation fixed point duality map iteration schemes 

分 类 号：O177.91[理学—数学]