Ákveðnum
Ákveðnum is an inflected form of the Icelandic adjective ákveðinn, a word meaning "certain, definite, determined." It is used to modify nouns when the noun is in the dative case, typically after prepositions that govern the dative, such as á (on, at) or í (in). In Icelandic grammar, adjectives decline to reflect case, number, gender, and definiteness, and ákveðnum represents one of these specific inflected forms.
In modern Icelandic, ákveðnum mainly appears in phrases describing definite or specific instances in the dative
Etymology and usage notes: the form ákveðnum is derived from the verb ákveða, meaning "to determine, decide."
See also: Icelandic grammar, adjectives, definite and indefinite forms, dative case.