A two-point counterexample to a common fixed point theorem in elliptic-valued suprametric spaces

Abstract

This independent correction-note preprint examines Theorem 2 of B. Alamri, Fixed Point Theorems in Elliptic-Valued Suprametric Spaces and Their Applications, Mathematics 14 (2026), 413 (doi:10.3390/math14030413). A complete two-point metric space, viewed as an elliptic-valued suprametric space, and two self-mappings satisfy the printed contractive hypothesis but have no common fixed point. The same construction disproves Corollaries 2 and 3. The obstruction is the exclusion of equal input points from the contraction condition; continuity or commutativity alone does not remove it. Exact rational calculations also contradict the claimed verifications in Examples 7 and 9, and the note clarifies an incorrect assertion about multiplication in the componentwise positive cone. The Volterra existence-and-uniqueness conclusion of Theorem 3 remains valid by an independent Banach contraction argument. Corollaries 1 and 4 are not disproved. The deposit contains the revised five-page PDF and a source ZIP with complete LaTeX, a standard-library Python script using exact arithmetic, verification output, and a README. The manuscript explicitly states that the counterexamples, proofs, theorem statements, and conclusions are the author’s responsibility and includes an account of AI assistance.