Approximate Fixed Point Sequences of Nonlinear Semigroup in Metric Spaces

Canadian mathematical bulletin

M. A. Khamsi¹ 

[1] Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968, USA

关键词: approximate fixed point;    fixed point;    hyperbolic metric space;    Ishikawa iterations;    nonexpansive mapping;    semigroup of mappings;    uniformly convex hyperbolic space;   

DOI  :  10.4153/CMB-2014-026-x

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

In this paper, we investigate the commonapproximate fixed point sequences of nonexpansive semigroups ofnonlinear mappings ${T_t}_{t geq 0}$, i.e., a family such that$T_0(x)=x$, $T_{s+t}=T_s(T_t(x))$, where the domain is a metric space$(M,d)$. In particular we prove that under suitable conditions, thecommon approximate fixed point sequences set is the same as the commonapproximate fixed point sequences set of two mappings from the family.Then we use the Ishikawa iteration to construct a common approximatefixed point sequence of nonexpansive semigroups of nonlinearmappings.

【 授权许可】

Unknown