On Banach fixed point theorems for partial metric spaces

By Ó. Valero. 2005

262 citations recorded by the source corpus.

In this paper we prove several generalizations of the Banach fixed point theorem for partial metric spaces (in the sense of O’Neill) given in, obtaining as a particular case of our results the Banach fixed point theorem of Matthews ([12]), and some well-known classical fixed point theorems when the partial metric is, in fact, a metric.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7799644943818d2e7f1c719b31e59bef32b3bd36

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In Geometry and Topology

1. E. Karapınar
2. Hassen Aydi
3. Pasquale Vetro
4. Mujahid Abbas
5. Bessem Samet
6. Stojan Radenovic
7. Talat Nazir
8. Zoran Kadelburg

Citations in the corpus

• SOME FIXED POINT RESULTS IN ORDERED PARTIAL METRIC SPACES (2011, background): “For more details, we refer the reader to [2, 4, 10, 13, 14, 16, 18, 19, 20, 22, 23].”
• Fixed point results under various contractive conditions in partial metric spaces (2013, unknown): “, [1,3–5,8,11,14,15,19,22]) studied fixed”
• 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].”
• Suzukiʼs type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces (2012, background): “First, we recall some definitions and some properties of partial metric spaces that can be found in [4,6,7,9,11].”
• A common fixed point theorem for cyclic operators on partial metric spaces (2012, unknown): “, [1] - [4],[7], [14]-[? ],[26, 33]).”
• A NOTE ON COMMON FIXED POINT THEOREMS IN PARTIAL METRIC SPACES (2011, background): “[1, 2, 8, 10–17, 20]) focused on this subject and generalized some fixed point theorems from the class of metric spaces to the class of partial metric spaces.”
• weak φ-contraction on partial metric spaces and existence of fixed points in partially ordered sets (2011, background): “5 (See [2, 4, 6]) Let (X, ) be a partially ordered set and (X, p) a complete partial metric space.”
• Fixed point results for generalized cyclic contraction mappings in partial metric spaces (2011, background): “Altun and Simsek [3], Oltra and Valero [17] and Valero [24] established some further generalizations of the results in [15], and Romaguera [20] proved a Caristi type fixed point theorem on partial metric spaces.”
• Be careful on partial metric fixed point results (2013, result): “Then, Valero [27], Oltra and Valero [21] and Altun, Sola and Simsek [4] gave some generalizations of the result of Matthews.”