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 asy...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.展开更多
基金the Ministry of Science and Technology of Spain,Grant BFM 2000-0344-CO2-01La Junta de Antalucia Project FQM-127
文摘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.
