Year: 2012
Author: Shaoyuan Xu, Wangbin Xu, Dingxing Zhong
Analysis in Theory and Applications, Vol. 28 (2012), Iss. 3 : pp. 269–277
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.3969/j.issn.1672-4070.2012.02.007
Analysis in Theory and Applications, Vol. 28 (2012), Iss. 3 : pp. 269–277
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 9
Keywords: piecewise polynomial interpolation deficient splines. iterated function system attractor generalized contractive mapping complete metric space fixed point.