A continuity obstruction and a corrected Volterra bound in perturbed F-metric fixed point results
Year: 2026
Type: preprint
Abstract: This independent technical comment examines selected statements of Alshehri and Ahmad, Axioms 15 (2026), 559 (https://doi.org/10.3390/axioms15080559). A complete perturbed metric space and a fixed-point-free self-map satisfy the hypotheses of Corollaries 4 and 5 under the paper's explicit Definition 7. Joint continuity provides a sufficient repair. The note also corrects the coefficient in the direct supremum norm contraction argument for the fractional Volterra application and gives explicit examples showing why the smaller coefficient does not ensure contraction, including a variant with a shared initial value. An interval mismatch in Example 7 is demonstrated by two explicit functions. The counterexample does not refute the main theorems with continuity retained, and the Volterra calculation does not disprove integral existence or uniqueness. Full proofs, the corrected bound, and an independent existence argument using operator iterates are included. Files: revised PDF and LaTeX source ZIP with an auxiliary verification script. Version 1.1. This is an independent comment, not an author-issued corrigendum or a journal-endorsed correction. The PDF includes an accurate statement of AI assistance and author responsibility.
Author: Zeraoulia, Rafik
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222869702
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