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00925njm 22002777a 4500 dc Estevan, Asier author Miñana, Juan-José author Valero, Oscar author 2019-10 The celebrated Kleene fixed point theorem is crucial in the mathematical modelling of recursive specifications in Denotational Semantics. In this paperwe discuss whether the hypothesis of the aforementioned result can be weakened. An affirmative answer to the aforesaid inquiry is provided so that a characterization of those properties that a self-mapping must satisfy in order to guarantee that its set of fixed points is non-emptywhen no notion of completeness are assumed to be satisfied by the partially ordered set. Moreover, the case in which the partially ordered set is coming from a quasi-metric space is treated in depth. Finally, an application of the exposed theory is obtained. Concretely, a mathematical method to discuss the asymptotic complexity of those algorithms whose running time of computing fulfills a recurrence equation is presented. Moreover, the aforesaid method retrieves the fixed point basedmethods that appear in the literature for asymptotic complexity analysis of algorithms. However, our new method improves the aforesaid methods because it imposes fewer requirements than those that have been assumed in the literature and, in addition, it allows to state simultaneously upper and lower asymptotic bounds for the running time computing. Estevan Asier, Miñana Prats Juan José, Valero Oscar. On fixed point theory in partially ordered sets and an application to asymptotic complexity of algorithms. Rev Real Acad Cienc Exactas Fis Nat Ser A-Mat. 2019 Oct;113(4):3233-3252. 10.1007/s13398-019-00691-8 1579-1505 1578-7303 Revista de la Real Academia de Ciencias Exactas Fisicas y Naturales Serie A-Matematicas http://hdl.handle.net/20.500.13003/14764 2-s2.0-85066026409 https://hdl.handle.net/20.500.12105/22817 483725900020 Partial order Quasi-metric Fixed point Kleene Asymptotic complexity Recurrence equation On fixed point theory in partially ordered sets and an application to asymptotic complexity of algorithms