Strong convergence of an new iterative method for a zero of accretive operator and nonexpansive mapping

Fixexd point theory and applications

Meng Wen¹  Changsong Hu¹ 

[1] Department of Mathematics, Hubei Normal University, Huangshi, P. R. China

关键词: MKC;    accretive operators;    the resolvent operator;    iterative method;    weakly continuous duality map;   

DOI  :  10.1186/1687-1812-2012-98

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Let E be a Banach space and A an m-accretive operator with a zero. Consider the iterative method that generates the sequence {x n } by the algorithm MathML, where {a n } and {r n } are two sequences satisfying certain conditions, MathML denotes the resolvent (I + r n A)-1 for r n > 0, F be a strongly positive bounded linear operator on E is MathML, and ϕ be a MKC on E. Strong convergence of the algorithm {x n } is proved assuming E either has a weakly continuous duality map or is uniformly smooth.

【 授权许可】

CC BY