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Volume 28, Issue 3
Some New Iterated Function Systems Consisting of Generalized Contractive Mappings

Shaoyuan Xu, Wangbin Xu & Dingxing Zhong

Anal. Theory Appl., 28 (2012), pp. 269-277.

Published online: 2012-10

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  • 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.

  • AMS Subject Headings

47H10, 54HA25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-28-269, author = {Shaoyuan Xu , Wangbin Xu , and Zhong , Dingxing}, title = {Some New Iterated Function Systems Consisting of Generalized Contractive Mappings}, journal = {Analysis in Theory and Applications}, year = {2012}, volume = {28}, number = {3}, pages = {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.

}, issn = {1573-8175}, doi = {https://doi.org/10.3969/j.issn.1672-4070.2012.02.007}, url = {http://global-sci.org/intro/article_detail/ata/4562.html} }
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.

Shaoyuan Xu , Wangbin Xu , and Zhong , Dingxing. (2012). Some New Iterated Function Systems Consisting of Generalized Contractive Mappings. Analysis in Theory and Applications. 28 (3). 269-277. doi:10.3969/j.issn.1672-4070.2012.02.007
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