Abstract
In this paper we consider the statistical manifold defined in terms of a deformed exponential \(\varphi \). For the non-atomic case we establish a relation between the behavior of the deformed exponential function and the \(\varDelta _2\)-condition and analyze the comportment of the normalizing function near to the boundary of its domain. In the purely atomic case we find an equivalent condition to the behavior that characterizes the deformed exponential discussed in this work. Moreover, we prove a consequence from the fact the Musielak-Orlicz function does not satisfy the \(\delta _2\)-condition.
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The authors would like to thank Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001, Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) (Procs. 309472/2017-2 and 408609/2016-8) and FUNCAP (Proc. IR7-00126-00037.01.00/17).
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Vieira, F.L.J., Vigelis, R.F., de Andrade, L.H.F., Cavalcante, C.C. (2019). Deformed Exponential and the Behavior of the Normalizing Function. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2019. Lecture Notes in Computer Science(), vol 11712. Springer, Cham. https://doi.org/10.1007/978-3-030-26980-7_28
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DOI: https://doi.org/10.1007/978-3-030-26980-7_28
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