TY - JOUR T1 - Some New Iterated Function Systems Consisting of Generalized Contractive Mappings AU - Shaoyuan Xu , AU - Wangbin Xu , AU - Zhong , Dingxing JO - Analysis in Theory and Applications VL - 3 SP - 269 EP - 277 PY - 2012 DA - 2012/10 SN - 28 DO - http://doi.org/10.3969/j.issn.1672-4070.2012.02.007 UR - https://global-sci.org/intro/article_detail/ata/4562.html KW - iterated function system, attractor, generalized contractive mapping, complete metric space, fixed point. AB -

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.