Cyclic Meir-Keeler Contraction and Its Fractals

In present times, there has been a substantial endeavor to generalize the classical notion of iterated function system (IFS). We introduce a new type of non-linear contraction namely cyclic Meir-Keeler contraction, which is a generalization of the famous Banach contraction. We show the existence and...

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Bibliographic Details
Published inNumerical functional analysis and optimization Vol. 42; no. 9; pp. 1053 - 1072
Main Authors Pasupathi, R., Chand, A. K. B., Navascués, M. A.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 04.07.2021
Taylor & Francis Ltd
Subjects
Cyclic Meir-Keeler contraction
fixed point
Fractal
Fractal interpolation function
Fractals
iterated function system
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Summary:In present times, there has been a substantial endeavor to generalize the classical notion of iterated function system (IFS). We introduce a new type of non-linear contraction namely cyclic Meir-Keeler contraction, which is a generalization of the famous Banach contraction. We show the existence and uniqueness of the fixed point for the cyclic Meir-Keeler contraction. Using this result, we propose the cyclic Meir-Keeler IFS in the literature for construction of fractals. Furthermore, we extend the theory of countable IFS and generalized IFS by using these cyclic Meir-Keeler contraction maps.
ISSN:0163-0563
1532-2467
DOI:10.1080/01630563.2021.1937215