Suresh Kumar, M.Murugan, V.2026-02-062021Journal of Physics: Conference Series, 2021, Vol.1850, 1, p. -17426588https://doi.org/10.1088/1742-6596/1850/1/012108https://idr.nitk.ac.in/handle/123456789/30119Given a non-empty subset X of the real line and a self map G on X, the functional equation representing G as an infinite linear combination of iterations of a self map g on X is known as the series-like functional equation. The solutions of the series-like functional equation have been studied only for the class of continuous strictly monotone functions. In this paper, we prove the existence of solutions of series-like functional equations for the class of continuous non-monotone functions using characteristic interval. © Published under licence by IOP Publishing Ltd.Characteristic IntervalFortIterative rootPM functions