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

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<b, with exact gap (37a^2+10ab+b^2)/36. It also proves failure near the diagonal for every integer n>=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.