## Abstract

The note is concerned with the functional equation

which is a generalised form of the so-called polynomial-like iterative equation. We investigate the existence of nondecreasing convex (both usual and higher order) solutions to this equation on open intervals using the Schauder fixed point theorem. The results supplement those proved by Trif (Aquat Math, 79:315–327, 2010) for the polynomial-like iterative equation by generalising them to a greater extent. This assertion is supported by some examples illustrating their applicability.

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The author is supported by the INSPIRE Faculty Fellowship of the Department of Science and Technology, India through DST/INSPIRE/04/2022/001760.

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Gopalakrishna, C. A note on convex solutions to an equation on open intervals.
*Aequat. Math.* **98**, 1151–1159 (2024). https://doi.org/10.1007/s00010-024-01038-4

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DOI: https://doi.org/10.1007/s00010-024-01038-4