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Vine's Expository Dictionary of NT Words [1]

1: Ἀπιστέω (Strong'S #569 — Verb — apisteo — ap-is-teh'-o )

"to be unbelieving" (a, negative, pistis, "faith;" cp. apistos, "unbelieving"), is translated "believed not," etc., in the AV (except in  1—Peter 2:7 , "be disobedient"); "disbelieve" (or "disbelieved") in the RV, in  Mark 16:11,16;  Luke 24:11,41;  Acts 28:24; "disbelieve" is the best rendering, implying that the unbeliever has had a full opportunity of believing and has rejected it; some mss. have apeitheo, "to be disobedient," in  1—Peter 2:7;  Romans 3:3 , RV, "were without faith;"  2—Timothy 2:13 , RV, "are faithless. Cp. Disobedient, C. See Believe

Webster's Dictionary [2]

(v. t.) Not to believe; to refuse belief or credence to; to hold not to be true or actual.