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Meir–Keeler-type conditions in abstract metric spaces

✍ Scribed by Zoran Kadelburg; Stojan Radenović

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
219 KB
Volume
24
Category
Article
ISSN
0893-9659

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✦ Synopsis

Various Meir-Keeler-type conditions for mappings acting in abstract metric spaces are presented and their connections are discussed. Results about associated symmetric spaces, obtained in [S. Radenović, Z. Kadelburg, Quasi-contractions on symmetric and cone symmetric spaces, Banach J. Math. Anal. 5 (2011), 38-50] are used to show that the regularity condition for the underlying cone can be dropped in some fixed point results that have appeared recently.

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On cyclic Meir–Keeler contractions in me
On cyclic Meir–Keeler contractions in metric spaces
✍ Bożena Piątek 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 212 KB

Cyclic Meir-Keeler contractions are considered under the recently introduced WUC and HW properties on pairs of subsets of metric spaces. We show that, in contrast with previous results in the theory, best proximity point theorems under these properties do not directly extend from cyclic contractions