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

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
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
preprint

Two fixed points and a nonuniform ratio argument in extended F-metric fixed point results

Zeraoulia Rafik
Zenodo (CERN European Organization for Nuclear Research)
Fixed Point Theorems Analysis
preprint

Two fixed points and a nonuniform ratio argument in extended F-metric fixed point results

Zeraoulia Rafik
preprint en

Abstract

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.

Zenodo (CERN European Organization for Nuclear Research)
Fixed Point Theorems Analysis
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Two fixed points and a nonuniform ratio argument in extended F-metric fixed point results — Zeraoulia Rafik · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS