BEST PROXIMITY FOR TWO PAIRS OF MAPPINGS IN MULTIPLICATIVE METRIC SPACE

. 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 speci  c  elds such as computer science or biology, where understanding the behavior of mappings is critical for modeling and analysis. Emphasizing the signi  cance of proximity in multiplicative metric spaces, the investigation seeks to unveil insights into the behavior and interaction of mappings, thereby o  ering valuable contributions to the broader  eld 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  elds, including di  erential equations, optimisation, and computer science, may be modelled by  xed-point equations of the type fx = 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.