Iagar, Razvan GabrielPuertas-Centeno, David2025-08-012025-08-012025-12Razvan Gabriel Iagar, David Puertas-Centeno, A new pair of transformations and applications to generalized informational inequalities and Hausdorff moment problem, Communications in Nonlinear Science and Numerical Simulation, Volume 151, 2025, 109091, ISSN 1007-5704, https://doi.org/10.1016/j.cnsns.2025.1090911878-7274 (online)1007-5704 (print)https://hdl.handle.net/10115/97597R. G. I. and D. P.-C. are very grateful to the Ministry of Science and Innovation of Spain for its partial financial support under Grants PID2020-115273GB-100 (AEI/FEDER, EU) and RED2022-134301-T funded by MCIN/AEI/10.13039/501100011033. D. P.-C. is also partially supported by the Grant PID2023-153035NB-100 funded by MICIU/AEI/10.13039/501100011033 and “ERDF/EU A way of making Europe”.classes of probability densities in R. These transformations have the property of interchanging the main informational measures such as 𝑝−moments, Shannon and Rényi entropies, and Fisher information. We thus apply them in order to establish extensions and generalizations of the Stam and moment-entropy inequalities in a mirrored domain of the entropic indexes. Moreover, with the aid of the two transformations we establish formal solutions to the Hausdorff entropic moment problem by connecting them with the solutions of the standard Hausdorff problem. In addition, we introduce a Fisher-like moment problem and relate it to the standard Hausdorff moment problem.enAttribution-NonCommercial 4.0 Internationalhttp://creativecommons.org/licenses/by-nc/4.0/Moment-entropy inequalityGeneralized stam inequalityShannon and Rényi entropiesFisher informationTransformationsHausdorff moment problemArticlehttps://doi.org/10.1016/j.cnsns.2025.109091info:eu-repo/semantics/openAccess