Cyclic Meir-Keeler Contraction and Its Fractals. (4th July 2021)

• Record Type: Journal Article
• Authors: Pasupathi, R.; Chand, A. K. B.; Navascués, M. A.
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 9(2021)
• Page Start: 1053
• Page End: 1072
• Publication Date: 2021-07-04
• Subjects: Cyclic Meir-Keeler contraction -- fixed point -- Fractal -- Fractal interpolation function -- iterated function system; 28A80 -- 37C25 -- 37C70 -- 47H04 -- 47H10 -- 54H25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1937215
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: 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.