Meir-Keeler-type conditions in abstract metric spaces. (English) Zbl 1220.54027

Kadelburg, Zoran; Radenović, Stojan

Appl. Math. Lett. 24, No. 8, 1411-1414 (2011).

Summary: 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 and Z. Kadelburg, Banach J. Math. Anal. 5, No. 1, 38–50, electronic only (2011; Zbl 1297.54058)] are used to show that the regularity condition for the underlying cone can be dropped in some fixed point results that have appeared recently.

MSC:

54H25	Fixed-point and coincidence theorems (topological aspects)
54E35	Metric spaces, metrizability

Keywords:

fixed point; abstract metric space; normal cone; regular cone; Meir-Keeler-type contractions

Citations:

Zbl 1297.54058

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