On multiplicative modular metric spaces of Kaplan et al.: corrections and clarifications

Kaplan et al. (J. Inequal. Appl. 2025:54, 2025) introduced the notion of multiplicative modular metric spaces, motivated by the framework of multiplicative metric spaces (Özavşar and Cevikel in J. Eng. Technol. Appl. Sci. 2(2):65–79, 2017) and the classical modular metric spaces established by Chistyakov (Nonlinear Anal. 72(1):1–14, 2010). However, upon closer analysis, it turns out that, under a domain for the modular parameter, their multiplicative modular metric is independent of the modular parameters. In particular, every multiplicative modular metric space of Kaplan et al. can be decomposed into a disjoint union of multiplicative metric spaces. In this paper, we propose a refinement of their definition by restricting the choice of the multiplicative modular parameter, and we demonstrate the resulting connection with modular metric spaces of Chistyakov. In addition, we analyze two fixed point theorems stated by Kaplan et al., construct explicit counterexamples to illustrate their failure, and provide corrected formulations of these results.