Fixed point theorems for some new nonlinear mappings in Hilbert spaces

Fixexd point theory and applications

Zenn-Tsun Yu¹  Chih-Sheng Chuang²  Lai-Jiu Lin² 

[1] Department of Electronic Engineering, Nan Kai University of Technology, Nantour, Taiwan;Department of Mathematics, National Changhua University of Education, Changhua, Taiwan

关键词: nonspreading mapping;    fixed point;    demiclosed principle;    ergodic theorem;    nonexpansive mapping;   

DOI  :  10.1186/1687-1812-2011-51

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we introduced two new classes of nonlinear mappings in Hilbert spaces. These two classes of nonlinear mappings contain some important classes of nonlinear mappings, like nonexpansive mappings and nonspreading mappings. We prove fixed point theorems, ergodic theorems, demiclosed principles, and Ray's type theorem for these nonlinear mappings. Next, we prove weak convergence theorems for Moudafi's iteration process for these nonlinear mappings. Finally, we give some important examples for these new nonlinear mappings.

【 授权许可】

CC BY