For those who are interested here is a definition (taken from the 1992
The Complete Word Study Dictionary)
πιστεύω
pisteúō; fut. pisteúsō, from pístis (πίστις), faith. To believe, have faith in, trust. NT meanings:
(I) Particularly, to be firmly persuaded as to something, to believe, followed by the inf. (Rom 14:2); by hóti (G3754), that (Mar 11:23; Rom 6:8; Rom 10:9). With the idea of hope and certain expectation (Act 18:8).
(A) More commonly used of words spoken and things, followed by the dat. of the person whose words one believes and trusts in (Mar 16:13; Joh 5:46; Act 8:12; 1Jn 4:1); by hóti (Joh 4:21).
(B) With an adjunct of the words or thing spoken, followed by the dat. (Luk 1:20; Joh 4:50; Act 24:14; 2Th 2:11; Act 13:41); by epí (G1909), upon, and the dat. (Luk 24:25); by en (G1722), in, and the dat. (Mar 1:15, "in the glad tidings" [a.t.], meaning to believe and embrace the glad tidings announced; Sept.: Psa 78:22; Jer 12:6).
(C) With an adjunct of the thing believed, followed by the acc. of thing (1Co 13:7; 1Jn 4:16). In the pass. (2Th 1:10). Followed by eis (G1519), unto, with the acc. (Joh 11:26; 1Jn 5:10); by hóti, that (Joh 14:10; Rom 10:9); by perí (G4012), about, concerning, and the gen. (Joh 9:18).
(D) Used in an absolute sense where the case of person or thing is implied from the context (Mat 24:23; Mar 13:21; Joh 12:47; Act 8:13 [cf. Act 8:12, Act 15:7]).
(II) Of God, to believe in God, to trust in Him as able and willing to help and answer prayer. Followed by the dat. of person with hóti, that (Act 27:25); by eis, in (Joh 14:1). Used in an absolute sense with the pres. part. pisteúontes, meaning if you believe (Rom 4:17-18; Heb 4:3). Generally, to believe in the declarations and character of God as made known in the gospel, with the dat. (Joh 5:24; Act 16:34; 1Jn 5:10). Followed by eis, in, with the acc., meaning to believe and rest upon, to believe in and profess (1Pe 1:21); by epí, on, with the acc. (Rom 4:24).
(III) Of a messenger from God, to believe on and trust in him (rather, when applied to a merely human messenger of God, to credit and trust him, as coming from God and acting under divine authority).
(A) Of John the Baptist, with the dat. (Mat 21:25, Mat 21:32; Mar 11:31; Luk 20:5).
(B) Of Jesus as the Messiah, able and ready to help His followers, followed by eis, in (Joh 14:1); to heal the sick and comfort the afflicted, with hóti, that (Mat 9:28); used in an absolute sense (Mat 8:13; Mar 5:36; Joh 4:48). (1) Generally of Jesus as a teacher and the Messiah sent from God. Followed by the dat. of person (Joh 5:38; Joh 8:31; Joh 10:37-38; Act 5:14; 2Ti 1:12); by hóti, that (Joh 8:24; Joh 11:27; Joh 13:19; Joh 16:27, Joh 16:30; Joh 17:8, Joh 17:21; Joh 20:31); by ginṓskō (G1097), to know (Joh 6:69; Joh 10:38); by eis, in, with the acc. of person meaning to believe and rest upon (Mat 18:6; Mar 9:42; Joh 2:11; Joh 3:15-16; Joh 4:39; Joh 6:35; Joh 7:5, Joh 7:38; Joh 8:30; Joh 17:20; Act 10:43; Act 19:4; Rom 10:14; Gal 2:16; 1Pe 1:8); figuratively, with tó phṓs (tó, neut. def, art.; phṓs [G5457], light), the light (Joh 12:36); tó ónoma (ónoma [G3686], name), the name, as to who Jesus is and what He has done (Joh 1:12; Joh 2:23; 1Jn 5:13); in the dat. (1Jn 3:23). Followed by epí, upon, with the acc. of person (Act 9:42; Act 11:17 [cf. Act 11:21]); with the dat. (Mat 27:42; 1Ti 1:16); figuratively (Rom 9:33; 1Pe 2:6, quoted from Isa 28:16); in the pass. (1Ti 3:16). (2) Used in an absolute sense, to believe, meaning to become a Christian (Mar 15:32; Luk 22:67; Joh 1:7; Joh 12:39; Act 4:4; Act 14:1; Act 17:12, Act 17:34). In the pres. part. pl. (hoi pisteúontes) or aor. part. pl. (hoi pisteúsantes), those who have believed, believers, Christians (Act 2:44; Act 4:32; Act 19:18; Rom 4:11; 1Co 1:21; Gal 3:22; 1Th 1:7; 1Pe 2:7).
(IV) Trans., to entrust, commit in trust to someone (Luk 16:11; Joh 2:24). In the pass., pisteúomai, with the acc. of thing, to be entrusted with something, to have something committed to one's trust or charge (Rom 3:2; 1Co 9:17; Gal 2:7; 1Th 2:4; 1Ti 1:11; Tit 1:3).
(V) Used in connection with the relationship between believing and miracle working.
(A) "And Jesus said unto them, Because of your unbelief: for verily I say unto you, If ye have faith as a grain of mustard seed, ye shall say unto this mountain, Remove hence to yonder place; and it shall remove: and nothing shall be impossible unto you" (Mat 17:20). This was what Jesus said to the disciples on His descent from the Mount of Transfiguration upon finding that they were unable to exorcise a boy's demon. This incident is given also in Mar 9:14-29 and Luk 9:37-43.
In Mat 17:17, when He said, ". . . O faithless and perverse generation," He did not include the disciples as unbelievers and perverse. The word for "faithless" is ápistos (G571), unbelieving, with the meaning of not trusting God to perform this and other miracles as opportunity and need arose.
What the father of the child said to Jesus explains how it is possible for him and the disciples to believe and, at the same time, to be beset by unbelief in accomplishing the task at hand. The father said, "I believe, Lord, help me in my unbelief" (a.t.).
Belief creates complete dependence upon the Lord and not independence. "Howbeit this kind goeth not out but by prayer and fasting" (Mat 17:21; see also Mar 9:29). The end result of this whole incident was "And they were all amazed at the mighty power of God" (Luk 9:43).
(B) "And all things whatsoever ye shall ask in prayer, believing, ye shall receive" (Mat 21:22). "Therefore I say unto you, What things soever ye desire, when ye pray, believe that ye receive them, and ye shall have them" (Mar 11:24). This latter assurance of the Lord also expresses dependence on the Lord through two words: proseuchómenoi (the pres. part. of proseúchomai [G4336], to pray to God) and aiteísthe (the subjunctive mid. of aitéomai [G154], to request as an inferior from a superior). It is not a desire at all but a humble request. This speaks not of the omnipotence of the believer's faith but of its full dependence upon God. "Believe that ye receive them, and ye shall have them," and, one could add, if the Lord consents to grant them.
(VI) The pres. part. ho pisteúōn (Joh 3:15-16, Joh 3:36; Joh 5:24; Joh 6:35, Joh 6:40, Joh 6:47; Joh 7:38; Joh 11:25-26; Joh 12:44, Joh 12:46; Joh 14:12) should not be taken as the one holding on to God constantly lest he would let loose and fall. It rather indicates that, once one believes, he continues to believe, for he has eternal life in him (Joh 3:15). The assurance Christ gave in Joh 10:28 is this: "And I give unto them eternal life; and they shall never perish, neither shall any man pluck them out of my hand." Once a believer places himself in Jesus, it is He who holds him firmly without someone being able to snatch him away, for if this could happen then there would be the acknowledgement that someone is mightier than Christ, which cannot be.
Syn.: peíthomai (G3982), to be convinced; hēgéomai (G2233), to deem, consider, think; epiginṓskō (G1921), to perceive, recognize.
Ant.: aporéō (G639), to be at a loss; diaporéō (G1280), to be much perplexed; distázō (G1365), to doubt, hesitate; apistéō (G569), to disbelieve; diakrínomai (G1252), to doubt, hesitate.