One of the research gaps in the study of best proximity for two pairs of mappings in multiplicative metric spaces may lie in the exploration of its applications in specific fields such as computer science or biology, where understanding the behavior of mappings is critical for modeling and analysis. Emphasizing the significance of proximity in multiplicative metric spaces, the investigation seeks
to unveil insights into the behavior and interaction of mappings, thereby offering valuable contributions to the broader field of mathematical analysis. Through rigorous theoretical analysis and computational experimentation, the study endeavors to provide actionable insights and methodologies for optimizing proximity in multiplicative metric spaces, thereby advancing the theoretical foundations and practical applications within this specialized domain. Many issues in many fields, including differential equations, optimisation, and computer science, may
be modelled by fixed-point equations of the type f x = x. In this work, two pairs
of proximally commuting mappings in a complete multiplicative metric space are
given the idea of optimal proximity. An example is also given to support the results.