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

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• 作者：Shaoyuan Xu ; Suyu Cheng ; Zuoling Zhou
• 关键词：Reich’s iterated function systems ; attractor ; Reich contractions ; complete metric spaces ; fixed point theory
• 刊名：Fixed Point Theory and Applications
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,298 KB
• 刊物主题：Analysis; Mathematics, general; Applications of Mathematics; Differential Geometry; Topology; Mathematical and Computational Biology;
• 出版者：Springer International Publishing
• ISSN：1687-1812

文摘

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.