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

Fixexd point theory and applications

Oscar Valero¹  Maryam A Alghamdi²  Mohammed A Alghamdi³  Naseer Shahzad³ 

[1] Department of Mathematics and Computer Science, University of Balearic Islands, Palma de Mallorca, Spain;Department of Mathematics, Faculty of Science - AL Faisaliah Campus, King Abdulaziz University, Jeddah, Saudi Arabia;Operator Theory and Applications Research Group, Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

关键词: topological poset;    extended quasi-metric;    Hausdorff;    monotone;    fixed point;    asymptotic complexity analysis;    06A06;    47H10;    54E50;    54H25;    54F05;    68Q25;   

DOI  :  10.1186/s13663-015-0419-x

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY