A Kirk Type Characterization of Completeness for Partial Metric Spaces

By Salvador Romaguera. 2009

301 citations recorded by the source corpus.

We extend the celebrated result of W. A. Kirk that a metric space is complete if and only if every Caristi self-mapping for has a fixed point, to partial metric spaces.

Subfields: Geometry and Topology, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/b2a373fdf85c985f8da0a8c5f65b4f1303db7afb

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In Geometry and Topology

In Management Science and Operations Research

Citations in the corpus

A SUZUKI TYPE FIXED POINT THEOREM FOR A GENERALIZED MULTIVALUED MAPPING ON PARTIAL HAUSDORFF METRIC SPACES (2013, background): “In fact, the (complete) partial metric spaces constitute a suitable framework to model several distinguished examples of the theory of computation and also to model metric spaces via domain theory, see [12, 16, 17, 19, 23, 28, 30, 33].”
Common fixed-point results for nonlinear contractions in ordered partial metric spaces (2011, background): “After that, fixed-point results in partial metric spaces have been studied [4,8,28,31,34,45].”
Fixed point results for generalized cyclic contraction mappings in partial metric spaces (2011, background): “Romaguera [24] proved a Caristi type fixed point theorem in partial metric spaces.”
FIXED POINT THEOREMS FOR GENERALIZED WEAKLY CONTRACTIVE CONDITION IN ORDERED PARTIAL METRIC SPACES (2011, background): “[4], Romaguera [24], Altun and Erduran [2] and Aydi [6, 7, 8].”
Fixed point results on metric and partial metric spaces via simulation functions (2015, background): “In this section we recall some definitions and some properties of partial metric spaces that can be found in [12, 13, 14, 15, 16].”
Matkowski's type theorems for generalized contractions on (ordered) partial metric spaces (2013, background): “Romaguera introduced in [18] the notions of a 0-Cauchy sequence in a partial metric space and of a 0-complete partial metric space.”
Suzukiʼs type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces (2012, methodology): “This will be done by means of the notion of 0-complete partial metric space which was introduced by Romaguera in [9].”
Be careful on partial metric fixed point results (2013, background): “Furthermore, Romaguera extended in [24] Kirk’s characterization of metric completeness [16] to partial metric spaces.”
Some Common Fixed Point Theorems in 0-σ-Complete Metric-Like Spaces (2013, methodology): “Romaguera [24] introduced the notion of 0-Cauchy sequence, 0-complete partial metric spaces and proved some characterizations of partial metric spaces in terms of completeness and 0-completeness.”
Various generalizations of metric spaces and fixed point theorems (2015, background): “Later, many authors studied partial metric spaces and their topological properties, as well as fixed point results in these spaces, see [68,93,96,113,121] and many others.”