Global convergence theorems of regularization iterative algorithm in uniformly smooth Banach spaces

• Published in: 2009 International Conference on Machine Learning and Cybernetics Vol. 4; pp. 2101 - 2105
• Main Authors: Shi, Jinwei, Zheng, Yaqin, Wang, Fuhai
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.07.2009
• Subjects: Accretive mapping; Convergence; Cybernetics; Global convergence theorem; Iterative algorithms; Machine learning; Pseudocontraction; Regularization iterative algorithm
• ISBN: 9781424437023; 1424437024
• ISSN: 2160-133X
• DOI: 10.1109/ICMLC.2009.5212138

Let E be a real uniformly smooth Banach space and A : D(A) sube E rarr 2 E be a m-accretive mapping which satisfies a linear growth condition of the form ||u|| les C (1 + ||x||) for some constant C > 0 and for all x isin E and u isin Ax, z isin D(A) be an arbitrary element. Suppose A -1 0 ne oslash. The sequence {x n } sub D(A) is generated from arbitrary x 0 isin D (A) by x n +l isin x n -lambda n (u n + thetas n (x n - z)), u n isin Ax n , n ges 0, where {lambda n } and {thetas n { are acceptably paired, then {x n { converges strongly to x* isin A - (0). As its application, we have deduced a strong convergence theorem for the iterative algorithm of fixed points for continuous pseudocontractions.