Strong fixed points of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg" display="inline" id="d1e121"><mml:mi>Φ</mml:mi></mml:math>-couplings and generation of fractals

Choudhury, Binayak S.; Chakraborty, Priyam

doi:10.1016/j.chaos.2022.112514

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Introduction and Mathematical Preliminaries2

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2023

2024

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Cited by 5 publications

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“…It has many versions in which different types of contractions have been utilized. Some instances of these works are noted in [8,22,25].…”

Section: Introduction and Mathematical Preliminariesmentioning

confidence: 99%

See 1 more Smart Citation

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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“…It has many versions in which different types of contractions have been utilized. Some instances of these works are noted in [8,22,25].…”

Section: Introduction and Mathematical Preliminariesmentioning

confidence: 99%

“…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%