An analogue of Nadler's result in Hardy-Rogers type iterated multifunction system. (6th September 2022) - Priya, M.; Navish, A.A.; Uthayakumar, R.
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.