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

Shaoyuan Xu & Wangbin Xu

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 anatural generalization of the well-known Banach contraction principle. In 2010, D. R. Sahuand A. Chakraborty introduced K-Iterated Function System using Kannan mapping whichwould cover a larger range of mappings. In this paper, following Hutchinson, D. R. Sahuand A. Chakraborty, we present some new iterated function systems by using the so-calledgeneralized contractive mappings, which will also cover a large range of mappings. Ourpurpose is to prove the existence and uniqueness of attractors for such class of iteratedfunction systems by virtue of a Banach-like fixed point theorem concerning generalizedcontractive mappings.

  • Keywords

iterated function system attractor generalized contractivemapping complete metric space fixed point

  • AMS Subject Headings

47H10 54HA25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-28-269, author = {Shaoyuan Xu and Wangbin Xu}, 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 anatural generalization of the well-known Banach contraction principle. In 2010, D. R. Sahuand A. Chakraborty introduced K-Iterated Function System using Kannan mapping whichwould cover a larger range of mappings. In this paper, following Hutchinson, D. R. Sahuand A. Chakraborty, we present some new iterated function systems by using the so-calledgeneralized contractive mappings, which will also cover a large range of mappings. Ourpurpose is to prove the existence and uniqueness of attractors for such class of iteratedfunction systems by virtue of a Banach-like fixed point theorem concerning generalizedcontractive 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 & Wangbin Xu JO - Analysis in Theory and Applications VL - 3 SP - 269 EP - 277 PY - 2012 DA - 2012/10 SN - 28 DO - http://dor.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 KW - attractor KW - generalized contractivemapping KW - complete metric space KW - fixed point AB - Iterated function systems (IFS) were introduced by Hutchinson in 1981 as anatural generalization of the well-known Banach contraction principle. In 2010, D. R. Sahuand A. Chakraborty introduced K-Iterated Function System using Kannan mapping whichwould cover a larger range of mappings. In this paper, following Hutchinson, D. R. Sahuand A. Chakraborty, we present some new iterated function systems by using the so-calledgeneralized contractive mappings, which will also cover a large range of mappings. Ourpurpose is to prove the existence and uniqueness of attractors for such class of iteratedfunction systems by virtue of a Banach-like fixed point theorem concerning generalizedcontractive mappings.
Shaoyuan Xu & Wangbin Xu. (1970). 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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