Title: An analogue of Nadler's result in Hardy-Rogers type iterated multifunction system

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

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

Abstract: The iterated multifunction system (IMS) provides a primary way of deriving a class of set-valued functions constructed on a complete metric space. An exemplification of the generalisation of single-valued function to set-valued function is the Hardy-Rogers type iterated function system (HR-IFS). In this regard, set-valued functions show their efficiency in various domains like robotics, preventive maintenance, control systems, and energy. We extend the notion of HR-IFS to a class of Hardy-Roger type iterated multifunction system (HR-IMS). Moreover, concentrating on tremendous applicability of fixed point theory in real-life scenario, we have obtained a fixed point of the newly constructed IMS with the aid of the Hutchinson-Barnsley theory. In the main result, the attractor of the HR-IMS is constructed in an unconventional way. Consequently, a common idea of the Banach contraction principle, known as Nadler's type result, is gleaned for our HR-IMS.

Keywords: iterated function system; IFS; iterated multifunction system; IMS; Hardy-Rogers type iterated multifunction system; HR-IMS; Nadler's result; attractor; fractal.

DOI: 10.1504/IJANS.2022.125307

International Journal of Applied Nonlinear Science, 2022 Vol.3 No.3, pp.223 - 241

Received: 30 Sep 2021
Accepted: 19 Apr 2022
Published online: 06 Sep 2022 *