2025/12/09 by R. Álvarez-Nodarse, K. Castillo, Álvarez-Nodarse, R. +1
Computer Science · Mathematics · #30C15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #Numerical Methods and Algorithms #math.CA #msc:30C15
paper · pdf · doi:10.48550/arxiv.2512.09004
Comment on https://doi.org/10.1016/j.jmaa.2025.130199
openalex publication_date 2025/12/09 · openalex created_date 2025/12/12 · arxiv created 2026/07/29 · arxiv updated 2026/07/31 · openalex updated_date 2026/08/03
After passage to the representing measure, the three principal theorems of Esstafa and Sfaxi, J. Math. Anal. Appl. 556 (2026), 130199, reduce respectively to Jensen's inequality, one quadratic identity, and a one-point measure. We solve the underlying reciprocal-moment problem sharply, determine all extremisers, and obtain a strictly stronger Hurwitz-zeta bound. We also identify the gap between formal inversion and evaluation at 1, and give explicit counterexamples to further analytic claims.