@article{Ri2026, 
author = {Song-Il Ri and Gwang-Jin O and Gyong-Jin Jo and Chol-U Pak and In-Son Ri},
title = {Key results obtained during the search for contractive mappings that can generate fractal interpolation functions},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {5},
pages = {13304-13338},
keywords = {fixed-point theorem, Bryant contraction mapping, Rakotch contraction mapping, iterated function systems (IFSs), fractal interpolation functions (FIFs)},
url = {https://www.sciopen.com/article/10.3934/math.2026549},
doi = {10.3934/math.2026549},
abstract = {In this paper, we show that, through two counterexamples, iterated function systems consisting of Bryant contraction mappings cannot generate fractals in general. Also, we present two new families of Rakotch contraction mappings that can generate new fractal interpolation functions with a wide range of applications in practice.}
}