FISHER-LIKE METRICS ASSOCIATED WITH Φ-DEFORMED NAUDTS ENTROPIES II

Dedicated to the memory of Professor Mihail Megan

Iulia-Elena Hirica^†, Cristina-Liliana Pripoae^‡, Gabriel-Teodor Pripoae^§, Vasile Preda^¶

Abstract: The paper continues our previous study on semi-Riemannian generalized Fisher metrics and Fisher-like metrics [26], in the framework of weighted Φ-deformed (Naudts) entropy. The associated scalar curvatures carry information related to the local structure of the space of the distributions of probability. The addition of some related group logarithms extends and refines results from the previously quoted paper on the non-weighted case.

Keywords: weighted Φ-deformed (Naudts) entropy, weighted divergence, weighted relative group entropy, weighted generalized Fisher metric, weighted Fisher-like metric.

MSC: 53B12, 22E70, 94A17, 53B20.

DOI 10.56082/annalsarscimath.2026.3.59

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^*Accepted for publication on March 11, 2026
^†ihirica@fmi.unibuc.ro, Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, RO-010014 Bucharest, Romania
^‡cristinapripoae@csie.ase.ro, Department of Applied Mathematics, The Bucharest University of Economic Studies, Piata Romana 6, RO-010374 Bucharest, Romania
^§gpripoae@fmi.unibuc.ro, Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, RO-010014 Bucharest, Romania
^¶vasilepreda0@gmail.com, Gheorghe Mihoc-Caius lacob Institute of Mathematical Statistics and Applied Mathematics of Romanian Academy, Calea 13 Septembrie, no. 13, RO-050711, Bucharest, Romania; Costin C. Kiritescu National Institute of Economic Research of Romanian Academy, Calea 13 Septembrie, no. 13, RO-050711, Bucharest, Romania; Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, RO-010014 Bucharest, Romania

PUBLISHED in

Annals Academy of Romanian Scientists Series on Mathematics and Its Application,

Volume 18 no 3, 2026

ISSN ONLINE 2066 – 6594
ISSN PRINT 2066 – 5997