Strong convergence of new iterative algorithms for certain classes of asymptotically pseudocontractions

作     者：Osilike, Micah Okwuchukwu Nwokoro, Peter Uche Chima, Eucharia Ezinwanne 

作者机构：Univ Nigeria Dept Math Nsukka Nigeria 

出 版 物：《FIXED POINT THEORY AND APPLICATIONS》 (Fixed Point Theory Appl.)

年 卷 期：2013年第2013卷第1期

页      面：1-19页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：asymptotically pseudocontractive maps fixed points strong convergence Hilbert spaces iterative algorithm 

摘      要：Let C be a nonempty closed convex subset of a real Hilbert space, and let T : C - C be an asymptotically k-strictly pseudocontractive mapping with F(T) = {x is an element of C : Tx = x} not equal = empty set. Let {alpha(n)}(n=1)(infinity) and {t(n)}(n=1)(infinity) be real sequences in (0, 1). Let {x(n)}(n=1)(infinity) be the sequence generated from an arbitrary x(1) is an element of C by {v(n) = P-C((1 - t(n))x(n)), n = 1, x(n+1) = (1 - alpha(n))v(n) + alpha(n)T(n)v(n), n = 1, where P-C : H - C is the metric projection. Under some appropriate mild conditions on {alpha(n)}(n=1)(infinity) and {t(n)}(n=1)(infinity), we prove that {x(n)}(n=1)(infinity) converges strongly to a fixed point of T. Furthermore, if T : C - C is uniformly L-Lipschitzian and asymptotically pseudocontractive with F(T) not equal empty set, we first prove that (I - T) is demiclosed at 0, and then prove that under some suitable conditions on the real sequences {a(n)}(n=1)(infinity), {beta(n)}(n=1)(infinity) and {t(n)}(n=1)(infinity) in (0, 1), the sequence {x(n)}(n=1)(infinity) generated from an arbitrary x(1) - C by {v(n) = PC((1 - t(n))x(n)), n = 1, y(n) = (1 - beta(n))v(n) + beta(n)T(n)v(n), n = 1, x(n+1) = (1 - alpha(n))v(n) + alpha(n)T(n)y(n), n = 1, converges strongly to a fixed point of T. No compactness assumption is imposed on T or C and no further requirement is imposed on F(T).