Speaker :- Dr. Pasupathi R

Title of the Talk :- A general framework for fractal interpolation functions

Date, Time and venue :- 22 April 2025, 5:00 PM - 6:40 PM at Seminar Hall, Dept of Mathematics.

About the speaker :- Dr. R. Pasupathi holds a Ph.D. in Mathematics with specialization in Fractal Analysis from the I.I.T. Madras. His research areas include Fractal Analysis, Fixed Point Theory, and Approximation Theory. He is particularly interested in the applications of Fixed Point Theory to the construction of fractal sets and the development of general frameworks for fractal interpolation approximation methods.

He has two years of postdoctoral research experience, including six months at IIT Madras (July 2022 – December 2022), six months at Transilvania University of Bra�?ov, Romania (February 2023 – August 2023), and more than one year at the Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Russia (October 2023 – December 2024). He has published 10 research papers in international refereed journals and 2 papers in international conference proceedings.

Abstract :- Fractal Interpolation Functions (FIFs) provide a recursive method for constructing interpolation functions using Iterated Function Systems (IFS) composed of Banach contractions. This talk presents two significant extensions to this classical framework.

Firstly, the construction of FIFs is generalized by incorporating weaker contractions, specifically Edelstein contractions, which encompass several important classes such as Matkowski, Meir-Keeler, F-contractions, and θ-contractions. This leads to a more flexible and inclusive approach to generating fractal interpolants.

Secondly, the theory is extended to general domains that are attractors of arbitrary IFSs, moving beyond standard Euclidean intervals or cubes. This unified framework enables the study of FIFs on a broader class of domains and supports comprehensive analytical investigations, including box dimension analysis.