Global convergence theorems of regularization iterative algorithm in uniformly smooth Banach spaces
Jinwei Shi, Yaqin Zheng, Fuhai Wang · 2009
Let E be a real uniformly smooth Banach space and A : D(A) sube E rarr 2Ebe 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-10 ne oslash. The sequence {xn} sub D(A) is generated from arbitrary x0isin D (A) by xn+l isin xn-lambdan(un+ thetasn(xn- z)), unisin Axn, n ges 0, where {lambdan} and {thetasn{ are acceptably paired, then {xn{ 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.