2015-04-2420130302-9743http://hdl.handle.net/10784/5244For the family of non-parametric q-exponential statistical models, in a former paper, written by the same authors, a differentiable Banach manifold modelled on Lebesgue spaces of real random variables has been built -- In this paper, the geometry induced on this manifold is characterized by q-divergence functionals -- This geometry turns out to be a generalization of the geometry given by Fisher information metric and Levi-Civita connections -- Moreover, the classical Amari´s α-connections appears as special case of the q−connections (q) -- The main result is the expected one, namely the zero curvature of the manifoldFor the family of non-parametric q-exponential statistical models, in a former paper, written by the same authors, a differentiable Banach manifold modelled on Lebesgue spaces of real random variables has been built -- In this paper, the geometry induced on this manifold is characterized by q-divergence functionals -- This geometry turns out to be a generalization of the geometry given by Fisher information metric and Levi-Civita connections -- Moreover, the classical Amari´s α-connections appears as special case of the q−connections (q) -- The main result is the expected one, namely the zero curvature of the manifoldengSpringer-Verlag Berlin Heidelbergarticleinfo:eu-repo/semantics/restrictedAccessALGORITMOSESPACIOS DE BANACHESPACIOS VECTORIALESTEOREMA DE BANACHGEOMETRÍA DE RIEMANNGEOMETRÍA DIFERENCIALESPACIOS MÉTRICOSMATEMÁTICASINTELIGENCIA ARTIFICIALPROCESAMIENTO DE IMÁGENESAlgorithmsBanach spacesVector spacesBanach- theoremGeometry, riemannianGeometry, differentialMetric spacesMathematicsArtificial intelligenceImage processingEspacios de OrliczAcceso restringido2015-04-24Loaiza Ossa, Gabriel IgnacioQuiceno Echavarría, Héctor Román10.1007/978-3-642-40020-9_82