Fractal set of generalized countable partial iterated function system with generalized contractions via partial Hausdorff metric

Priya, M.; Uthayakumar, R.

doi:10.1016/j.topol.2022.108000

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Introduction and Mathematical Preliminaries1

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2022

2024

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Cited by 5 publications

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“…In later research the theory has been extended, modified and applied in the framework of different mathematical spaces for obtaining fractals. Some instances of these works are in references [3,8,22,25,26].…”

Section: Introduction and Mathematical Preliminariesmentioning

confidence: 99%

Fixed points of generalized cyclic contractions without continuity and application to fractal generation

Roy,

Saha,

Ghosh

et al. 2023

NAMC

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In this paper, we define a generalized cyclic contraction and prove a unique fixed point theorem for these contractions. An illustrative example is given, which shows that these contraction mappings may admit the discontinuities and also that an existing result in the literature is effectively generalized by the theorem. We apply the fixed point result for generation of fractal sets through construction of an iterated function system and the corresponding Hutchinsion–Barnsley operator. The above construction is illustrated by an example. The study here is in the context of metric spaces.

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