Liz Marzán, EduardoBuedo Fernández, Sebastián2019-07-102020-01-102019-01-10Liz, E. & Buedo-Fernández, S. A new formula to get sharp global stability criteria for one-dimensional discrete-time models. Qual. Theory Dyn. Syst. 18,813-824 (2019). doi: 10.1007/s12346-018-00314-41575-5460http://hdl.handle.net/10347/19096This is a post-peer-review, pre-copyedit version of an article published in Qualitative Theory of Dynamical Systems. The final authenticated version is available online at: https://doi.org/10.1007/s12346-018-00314-4We present a new formula that makes it possible to get sharp global stability results for one-dimensional discrete-time models in an easy way. In particular, it allows to show that the local asymptotic stability of a positive equilibrium implies its global asymptotic stability for a new family of difference equations that finds many applications in population dynamics, economic models, and also in physiological processes governed by delay differential equations. The main ingredients to prove our results are the Schwarzian derivative and some dominance argumentseng© Springer Nature Switzerland AG 2019Global stabilityDiscrete-time modelMackey-Glass equationGamma-modelSchwarzian derivativeMaterias::Investigación::12 Matemáticas::1202 Análisis y análisis funcional::120207 Ecuaciones en diferenciasjournal article10.1007/s12346-018-00314-41662-3592open access