On fixed point theory in topological posets, extended quasi-metric spaces and an application to asymptotic complexity of algorithms

In 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. Fi...

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Bibliographic Details
Published in:Fixed point theory and algorithms for sciences and engineering Vol. 2015; no. 1; pp. 1 - 13
Main Authors: Shahzad, Naseer, Valero, Oscar, Alghamdi, Mohammed A, Alghamdi, Maryam A
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 06.10.2015
Springer Nature B.V
Subjects:
Algorithms
Analysis
Applications of Mathematics
Asymptotic properties
Complexity
Differential Geometry
Fixed points (mathematics)
Mathematical analysis
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
New Challenges and Trends in Fixed Point Theory and Its Applications
Run time (computers)
Set theory
Topology
Upper bounds
68Q25
47H10
54E50
fixed point
asymptotic complexity analysis
topological poset
Hausdorff
06A06
extended quasi-metric
monotone
54H25
54F05
ISSN:1687-1812, 1687-1812, 2730-5422
Online Access:Get full text
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Summary:In 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.
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ISSN:1687-1812
1687-1812
2730-5422
DOI:10.1186/s13663-015-0419-x