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 05822501
)] are used to show that the regularity condition for the underlying cone can be dropped in some fixed point results that have appeared recently.