Title: A novel attractor for an IFS having generalised contractions in dislocated quasi metric space

Authors: M. Priya; A.A. Navish; R. Uthayakumar

Addresses: Department of Mathematics, The Gandhigram Rural Institute – Deemed to be University, Gandhigram, Dindigul, Tamil Nadu – 624 302, India ' Department of Mathematics, The Gandhigram Rural Institute – Deemed to be University, Gandhigram, Dindigul, Tamil Nadu – 624 302, India ' Department of Mathematics, The Gandhigram Rural Institute – Deemed to be University, Gandhigram, Dindigul, Tamil Nadu – 624 302, India

Abstract: Fixed point theory has a wide application in mathematics and this article initially builds a modern fixed point theorem for generalised contractive type functions on a complete dislocated quasi metric space (DQMS, in short). A standard procedure for appraising the attractor of an iterated function system (IFS, simply) is working with fixed point theory and performing the Hutchinson-Baransley theory (in brief, HB theory) and in the perspective of this theorem, an IFS comprising a finite number of generalised contractive mappings is considered. Also, it can be appraised that the parameters of the contraction functions of a fractal image through an IFS and as a consequence of this process, one can synthesise it, calling it an inverse problem. Finally, the conventional HB theory is performed. As a result of this, we picked up an attractor (fractal) as a fixed point of the HB operator.

Keywords: dislocated quasi metric space; generalised contractive mapping; HB theory; attractor; fractal; iterated function system.

DOI: 10.1504/IJANS.2024.141351

International Journal of Applied Nonlinear Science, 2024 Vol.4 No.3, pp.210 - 227

Received: 20 Aug 2022
Accepted: 15 Dec 2022
Published online: 09 Sep 2024 *

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