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A note on lower bounds for numerical series

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

Abstract

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.

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