Reich’s iterated function systems and well-posedness via fixed point theory

Fixexd point theory and applications

Shaoyuan Xu¹  Suyu Cheng²  Zuoling Zhou³ 

[1] Department of Mathematics and Statistics, Hanshan Normal University, Chaozhou, China;Library, Hanshan Normal University, Chaozhou, China;School of Lingnan, Zhongshan University, Guangzhou, China

关键词: Reich’s iterated function systems;    attractor;    Reich contractions;    complete metric spaces;    fixed point theory;    47H10;    54HA25;   

DOI  :  10.1186/s13663-015-0320-7

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we prove the existence of the attractors for Reich’s iterated function systems by virtue of a Banach-like fixed point theorem. As a result, under the condition that the Reich contractions discussed are continuous, we give an affirmative answer to an open question posed by Singh et al. in 2009. In addition, we formulate a collage theorem for Reich’s iterated function systems.

【 授权许可】

CC BY