A finite counterexample to two best proximity point theorems in non-Archimedean generalized Menger spaces

Abstract

This independent correction-note preprint examines Theorems 1 and 2 of Oumertou et al., Mathematics 14 (2026), 1443 (doi:10.3390/math14091443). A complete six-point non-Archimedean generalized Menger space and a cyclic mapping satisfy the printed hypotheses, including proximal admissibility on A0, but have no best proximity point. The note identifies the mismatch between the cross-set contraction definition and its use on triples within A0, gives an explicit contradiction to the claimed proof step, and proves that adding admissibility on all three proximal sets alone cannot repair the theorem for sets with empty common intersection. Direct calculations also show defects in Examples 2 and 8; Example 3 inherits the ambient-space defect of Example 2. No independent disproof of Theorem 3 is asserted. The deposit contains the six-page manuscript and its LaTeX source with a dependency-free exact Python verification script and verification output. The manuscript includes a disclosure of substantive AI assistance.