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Viscosity approximation method for accretive operator in Banach space
Authors:Rudong Chen  Zhichuan Zhu
Institution:Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300160, PR China
Abstract:Let XX be a uniformly smooth Banach space, CC be a closed convex subset of XX, and AA an m-accretive operator with a zero. Consider the iterative method that generates the sequence {xn}{xn} by the algorithm
xn+1=αnf(xn)+(1−αn)Jrnxn,xn+1=αnf(xn)+(1αn)Jrnxn,
where αnαn and γnγn are two sequences satisfying certain conditions, JrJr denotes the resolvent (I+rA)−1(I+rA)1 for r>0r>0, and f:C→Cf:CC be a fixed contractive mapping. Then as n→∞n, the sequence {xn}{xn} strongly converges to a point in F(A)F(A). The results presented extends and improves the corresponding results of Hong-Kun Xu Strong convergence of an iterative method for nonexpansive and accretive operators, J. Math. Anal. Appl. 314 (2006) 631–643].
Keywords:Accretive operator  Uniformly smooth  Fixed point  Banach limit
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