1) to fix the eyes on, gaze upon
2) to look into anything
3) metaphorically to fix one's mind on one as an example
Part of Speech: verb
From a compound of G1 (as a particle of union) and τείνω teinô (to stretch); to gaze intently: - behold earnestly (stedfastly), fasten (eyes), look (earnestly, stedfastly, up stedfastly), set eyes.
These two sites give similar information, with the definition from several dictionaries and statistics on the use of the word.
Perseus Digital Library
University of Chicago's Logion lexicon
Thayer's dictionary plus other information.
From this site's dictionary (in Italian)
Click on the first column to search for that word as a form of the root ἀτενίζω; click on the second column to search for that grammatical form of the root ἀτενίζω; click on the third column to search for that word and grammatical form; click on the total to search for the root ἀτενίζω.