Best Proximity Point Results in Non-Archimedean Fuzzy Metric Spaces

When two sets do not necessarily intersect, how can we identify a point that realizes the smallest attainable distance between them?

The study examines different contractive conditions in a non-Archimedean fuzzy metric space and derives best-proximity-point existence and uniqueness results.

• Define the space and proximity structure
• Establish contractive conditions
• Prove existence and uniqueness
• Use examples to support the theorems

The paper establishes best-proximity-point existence and uniqueness results under specified contractive conditions and provides examples illustrating the theorems.

The problem illustrates a useful general idea: when an exact solution or intersection is unavailable, the target can be the closest attainable state. That pattern is conceptually relevant to approximation, optimization, and decision problems.