Strong convergence of approximating fixed points for nonexpansive nonself-mappings in Banach spaces

Kodai Mathematical Journal

Tae Hwa Kim¹  Jong Soo Jung¹ 

关键词: Nonexpansive mapping;    fixed points;    boundary conditions;    weak inwardness;    Banach limits;    sunny and nonexpansive retraction;   

DOI  :  10.2996/kmj/1138043939

学科分类：数学（综合）

来源: Tokyo Institute of Technology, Department of Mathematics

【 摘 要 】

References(27)Let E be a reflexive Banach space with a uniformly Gâteaux differentiable norm, C a nonempty closed convex subset of E, and T C→E a nonexpansive mapping satisfying the inwardness condition. Assume that every weakly compact convex subset of E has the fixed point property. For u∈C and t∈(0, 1), let xt be a unique fixed point of a contraction Gt C→E, defined by Gtx=tTx+(1−t)u, x∈C. It is proved that if {xt} is bounded, then the strong limt→1xt exists and belongs to the fixed point set of T Furthermore, the strong convergence of other two schemes involving the sunny nonexpansive retraction is also given in a reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm.

【 授权许可】

Unknown