Extend A_d-contractions to best proximity points for non-self mappings

Extend the A_d-contraction framework to obtain best proximity point results for non-self mappings, identifying appropriate conditions under which best proximity points exist within the A_d-controlled dislocated metric setting.

Background

The paper introduces the class of A_d-contractions tailored to dislocated metric spaces and establishes fixed point theorems for single mappings, sequences of mappings, and integral-type contractions. Best proximity points generalize fixed points to non-self mappings (e.g., when a mapping acts between distinct subsets), ensuring optimal proximity when an actual fixed point may not exist.

Extending the A_d framework from fixed point results to best proximity points would require identifying suitable contractive-type conditions and structural assumptions compatible with dislocated metrics, where self-distances can be nonzero and additional axioms (such as A3) are used to secure uniqueness in the fixed point case.