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PreprintCC BY 4.0Zenodo

Mathematical Corrections to the Special-Mean Application and Cubic Example in New Approaches to Fractal–Fractional Bullen's Inequalities Through Generalized Convexity

  • Rafik Zeraoulia
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Abstract

This independent correction note examines the printed special-mean application (Proposition 2), the cubic illustration (Equations 13–14), and the kernel normalization in Saleh et al., Fractal and Fractional 9 (2025), Article 25, doi:10.3390/fractalfract9010025. At nu=1 and n=2, it proves a strict violation of Proposition 2 for every 0<a=2, supplies a self-contained corrected classical power-mean estimate, repairs the cubic formulas, and records the required positive kernel mass. These findings do not establish falsity of the main nonclassical theorems for 0<nu<1. The deposit includes the five-page manuscript PDF and a LaTeX source ZIP with exact symbolic verification code. This is an independent preprint, not a publisher-issued corrigendum.

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Cite

BibTeXRIS
BibTeX
@misc{zeraoulia2026mathematical,
  title = {{Mathematical Corrections to the Special-Mean Application and Cubic Example in New Approaches to Fractal–Fractional Bullen's Inequalities Through Generalized Convexity}},
  author = {Rafik Zeraoulia},
  howpublished = {Zenodo},
  year = {2026},
  month = oct,
  doi = {10.5281/zenodo.23438306},
  url = {https://zenodo.org/records/23438306},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Mathematical Corrections to the Special-Mean Application and Cubic Example in New Approaches to Fractal–Fractional Bullen's Inequalities Through Generalized Convexity
AU  - Rafik Zeraoulia
PY  - 2026
DA  - 2026/10/17
PB  - Zenodo
DO  - 10.5281/zenodo.23438306
UR  - https://zenodo.org/records/23438306
AB  - This independent correction note examines the printed special-mean application (Proposition 2), the cubic illustration (Equations 13–14), and the kernel normalization in Saleh et al., Fractal and Fractional 9 (2025), Article 25, doi:10.3390/fractalfract9010025. At nu=1 and n=2, it proves a strict violation of Proposition 2 for every 0<a=2, supplies a self-contained corrected classical power-mean estimate, repairs the cubic formulas, and records the required positive kernel mass. These findings do not establish falsity of the main nonclassical theorems for 0<nu<1. The deposit includes the five-page manuscript PDF and a LaTeX source ZIP with exact symbolic verification code. This is an independent preprint, not a publisher-issued corrigendum.
ER  -