Shahzad, NaseerValero, OscarAlghamdi, Mohammed AAlghamdi, Maryam A2024-07-042024-07-042015-10-06Shahzad N, Valero O, Alghamdi MA, Alghamdi Maryam A. On fixed point theory in topological posets, extended quasi-metric spaces and an application to asymptotic complexity of algorithms. Fixed Point Theory Appl. 2015 Oct 06;:179.1687-1812http://hdl.handle.net/20.500.13003/10666http://hdl.handle.net/20.500.12105/20150In this paper we present a few fixed point results in the framework of topological posets. To this end, we introduce an appropriate notion of completeness and order-continuity. Special attention is paid to the case that the topology of the topological poset is induced by an extended quasi-metric. Finally, the applicability of the exposed results is illustrated providing a methodology to determine the asymptotic upper bound of the complexity of those algorithms whose running time of computing is the solution to a special type of recurrence equation.enghttp://creativecommons.org/licenses/by/4.0/Topological posetExtended quasi-metricHausdorffmonotoneFixed pointAsymptotic complexity analysisresearch articleAttribution 4.0 International17910.1186/s13663-015-0419-xFixed Point Theory and Applicationsopen access2-s2.0-84943652398366020200001