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

Shaoyuan Xu and Wangbin Xu

10.3969/j.issn.1672-4070.2012.02.007

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

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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.

  • History

Published online: 2012-10

  • AMS Subject Headings

47H10, 54HA25

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