αἰνέω
This is a Poet. and ionic Verb, while ἐπαινέω is used in attic Prose
I. properly, "to tell or speak of" (cf. αἶνος), Aesch.
II. commonly, "to speak in praise of, praise", Lat. laudo, c. acc., Hom., Hdt.
2. "to allow, recommend", Od.: c. inf. "to recommend" to do a thing, Aesch.; also c. part., αἰνεῖν ἰόντα "to commend" one's going, id=Aesch.
3. like ἀγαπάω, "to be content, acquiesce", Eur.:—c. acc. rei, "to be content with, acquiesce in", γάμον Pind., etc.; θῆσσαν τράπεζαν Eur.
4. "to decline courteously", Hes.
III. "to promise or vow", τί τινι or τινὶ ποιεῖν τι Soph., Eur.