SOME NEW ITERATED FUNCTION SYSTEMS CONSISTING OF GENERALIZED CONTRACTIVE MAPPINGS

Iterated function systems （IFS） were introduced by Hutchinson in 1981 as a natural generalization of the well-known Banach contraction principle. In 2010, D. R. Sahu and A. Chakraborty introduced K-Iterated Function System using Kannan mapping which would cover a larger range of mappings. In this pa...

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Bibliographic Details
Published in分析理论与应用：英文刊 Vol. 28; no. 3; pp. 269 - 277
Main Author Shaoyuan Xu Wangbin Xu Dingxing Zhong
Format Journal Article
LanguageChinese
Published 2012
Subjects
Banach
IFS
不动点
压缩原理
定理证明
广义压缩映射
覆盖
迭代函数系统
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ISSN1672-4070
1573-8175

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Summary:Iterated function systems （IFS） were introduced by Hutchinson in 1981 as a natural generalization of the well-known Banach contraction principle. In 2010, D. R. Sahu and A. Chakraborty introduced K-Iterated Function System using Kannan mapping which would cover a larger range of mappings. In this paper, following Hutchinson, D. R. Sahu and A. Chakraborty, we present some new iterated function systems by using the so-called generalized contractive mappings, which will also cover a large range of mappings. Our purpose is to prove the existence and uniqueness of attractors for such class of iterated function systems by virtue of a Banach-like fixed point theorem concerning generalized contractive mappings.
Bibliography:32-1631/O1
Iterated function systems （IFS） were introduced by Hutchinson in 1981 as a natural generalization of the well-known Banach contraction principle. In 2010, D. R. Sahu and A. Chakraborty introduced K-Iterated Function System using Kannan mapping which would cover a larger range of mappings. In this paper, following Hutchinson, D. R. Sahu and A. Chakraborty, we present some new iterated function systems by using the so-called generalized contractive mappings, which will also cover a large range of mappings. Our purpose is to prove the existence and uniqueness of attractors for such class of iterated function systems by virtue of a Banach-like fixed point theorem concerning generalized contractive mappings.
iterated function system, attractor, generalized contractive mapping, completemetric space, fixed point
ISSN:1672-4070
1573-8175