An analogue of Nadler's result in Hardy-Rogers type iterated multifunction system. (6th September 2022)

• Record Type: Journal Article
• Authors: Priya, M.; Navish, A.A.; Uthayakumar, R.
• Is Part Of: International journal of applied nonlinear science. Volume 3:Number 3(2022)
• Page Start: 223
• Page End: 241
• Publication Date: 2022-09-06
• Subjects: iterated function system -- IFS -- iterated multifunction system -- IMS -- Hardy-Rogers type iterated multifunction system -- HR-IMS -- Nadler's result -- attractor -- fractal; Science -- Mathematical models -- Periodicals; Engineering -- Mathematical models -- Periodicals; Nonlinear theories -- Periodicals; 501.5118
• Languages: English
• ISSNs: 1752-2862

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.