Fractal Attractor via Controlled Strong b-Kannan Iterated Function System

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DOI: https://doi.org/10.28924/2291-8639-23-2025-155
Published: Jun 26, 2025
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M. Dhanzeem Ahmed, D. Easwaramoorthy, Fractal Attractor via Controlled Strong b-Kannan Iterated Function System, Int. J. Anal. Appl., 23 (2025), 155.

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M. Dhanzeem Ahmed, D. Easwaramoorthy

Abstract

Nowadays, most of the real time problems have been attempted by using well-known fixed point theorems. Especially the Banach contraction theorem is a well-posted tool to solve many dynamical problems of applied mathematics. This paper explores an idea in generalizing fixed point theorem to generate a proposed fractal type set called Controlled Strong b−Kannan Fractal (CSbK-Fractal) through the dynamical system of Kannan contractivity function in the Controlled Strong b−Metric Space (CSbMS). Furthermore, the collage type theorem is proved on CSbK-Fractal. In this context, the interesting results and consequences of newly developing iterated function system and its fractal attractor in the controlled strong b−metric space are discussed with examples. This theory can provide a novel direction to construct a new kind of fractal set in generalized spaces.

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