Fixed point theorems in quasi-metric spaces and the specialization partial order


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	Fixed point theorems in quasi-metric spaces and the specialization partial order


	Fixed Point Theory, Volume 19, No. 2, 2018, 733-750, June 1st, 2018 DOI: 10.24193/fpt-ro.2018.2.55 Authors: Naseer Shahzad and Oscar Valero Abstract: In this paper we present a new fixed point theorem in quasi-metric spaces which captures the spirit of Kleene's fixed point theorem. To this end, we explore the fundamental assumptions in the aforesaid result when we consider quasi-metric spaces endowed with the specialization partial order. Thus, we introduce an appropriate notion of order-completeness and order-continuity that ensure the existence of fixed point with distinguished properties. Moreover, some fixed point theorems are derived as a particular case of our main result when the self-mappings under consideration satisfy, in addition, any type of Banach contractive condition under different quasi-metric notions of completeness. Key Words and Phrases: quasi-metric, specialization partial order, order-completeness, fixed point, monotonicity, order-continuity, contraction. 2010 Mathematics Subject Classification: 06A06, 47H09, 47H10, 54E50, 54F05, 68N30. Published on-line: June 1st, 2018. Abstract pdf Fulltext pdf Back to volume's table of contents