Two fixed points and a nonuniform ratio argument in extended F-metric fixed point results
This independent technical comment examines selected uniqueness assertions and a convergence argument in Badriah Alamri’s Fractal and Fractional 10 (2026), 261 (doi:10.3390/fractalfract10040261). The mapping in Example 3 has exactly two fixed points, zero and 4/3. The note distinguishes a literal inconsistency in the comparison-function definition from the intended nondecreasing convention, and shows that correcting that convention alone does not validate the restricted uniqueness hypothesis of Theorem 4. A metric specialization supplies a counterexample under the intended convention; an equality-order example exposes the analogous issue in Corollary 4. An elementary positive array disproves the uniform ratio-test inference used in the existence proof, without purporting to refute existence itself. The continuous Volterra conclusion of the fractional application is recovered directly by Banach’s contraction principle. Version 1.1. Includes the complete PDF and a source ZIP with LaTeX source and auxiliary exact-arithmetic checks. The note includes an AI-assistance and author-responsibility declaration. This is an independent comment, not an author-issued corrigendum or a journal-endorsed correction.
Authors
- Zeraoulia Rafik (ORCID: https://orcid.org/0000-0002-5436-3320)
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-10-18
- DOI
- https://doi.org/10.5281/zenodo.23460253
- Primary Topic
- Fixed Point Theorems Analysis
- Type
- preprint