A new contribution to the fixed point theory in partial quasi-metric spaces and its applications to asymptotic complexity analysis of algorithms

In this paper we continue the study of fixed point theory in partial quasi-metric spaces and its usefulness in complexity analysis of algorithms. Concretely we prove two new fixed point results for monotone and continuous self-mappings in 0-complete partial quasi-metric spaces and, in addition, we show that the assumptions in the statement of such results cannot be weakened. Furthermore, as an application, we present a quantitative fixed point technique which is helpful for asymptotic complexity analysis of algorithms.