More on Fixed Point Theorem of {a, b, c}-Generalized Nonexpansive Mappings in Normed Spaces

被引：1

作者：

Sahar Mohamed Ali ^{[1
,2
]}

机构：

[1] Department of Mathematics, Faculty of Science, Ain Shams University

[2] Egypt & General Courses Department, Riyadh Philanthropic Society for Science, Prince Sultan University, College for Women

来源：

AnalysisinTheoryandApplications | 2013年 / 29卷 / 01期

关键词：

Fixed point theorem; {a; b; c}-generalized-nonexpansive mapping; asymptotic center; Browder ’s strong convergence Theorem;

D O I：

暂无

中图分类号：

O177.91 [非线性泛函分析];

学科分类号：

070104 ;

摘要：

Let X be a weakly Cauchy normed space in which the parallelogram law holds, C be a bounded closed convex subset of X with one contracting point and T be an {a, b, c}-generalized-nonexpansive mapping from C into C. We prove that the infimum of the set { ||x-T(x)|| } on C is zero, study some facts concerning the {a,b,c}-generalized-nonexpansive mapping and prove that the asymptotic center of any bounded sequence with respect to C is singleton. Depending on the fact that the {a,b,0}-generalized-nonexpansive mapping from C into C has fixed points, accordingly, another version of the Browder 's strong convergence theorem for mappings is given.

引用

页码：1 / 11

页数：11