In the Greek translations of the Scriptures there are two words sometimes translated by the English word ‘worship’. One, «latreuo», is used always of the Absolute Being, the Eternal. The other, «proskuneo», does not mean ‘worship’ in the modern sense of the word, but rather a show of deep respect by bowing on knees and kissing the feet or fringe of a garment. It is something like the deep bow of the Japanese, but more closely to that practice in the Middle East of fully bowing on knees to kiss the feet or hand of someone worthy or demanding deep respect.

In the Jewish Greek version of the Old Testament – Septuagint – LXX, the word «proskuneo» is used when someone bows or prostrates to the ground, on knees or face, in deep respect for another. Examples of this can be seen in

1 Samuel 24:9 [Septuagint - LXX]
David bowed with his face to the ground and did obeisance {prosekunesen} to king Saul.

And, again, in the case of Abigail when she saw David, 

1 Samuel 25:23 [Septuagint - LXX]
And Abigail saw David, and she hasted and alighted from her ass; and she fell before David on her face, and did obeisance to him {prosekunesen}, bowing to the ground." 

It would seem clear that in these two cases «proskuneois» is not ‘worship’ in the modern sense of the word, but rather a deep respect common in the Eastern world, and unknown in the Western.

In the Nazarene Writings (known as the New Testament) «proskuneo» is used as described above, that is a bowing or kneeling in deep respect. This can be seen in a number of verses which are here listed:

Matthew 18:26 [Hebraic Roots Bible - HRB]
26 Then having fallen down, the slave bowed the knee to him{proskuneo}, saying, Master, have patience with me, and I will pay all to you.
(Yeshua's words in purple)
Mark 15:19 [Moffatt New Testament - 1913]
They(the soldiers) struck him on the head with a stick and spat upon him and bent their knees to him in homage{proskuneo}.
Acts 10:25-26 [The Scriptures - TS]
25 And it came to be, that when Kepha{Peter} entered, Cornelius met him and fell down at his feet and bowed before him{proskuneo}. 
26 But Kepha raised him up, saying, “Stand up, I myself am also a man"
Revelation 3:9 [HRB]
9 Behold, I give out of the synagogue{congregation} of Satan those saying themselves to be Jews, and they are not, but they lie. Behold, I will make them come and bow down before your feet{proskuneo}, and they shall know that I loved you.

It is true the word «proskuneo» may be used more like the modern English meaning of ‘worship’ — veneration of a deity. This can be seen in the Greek translator’s rendering of Yeshua’s words to the Samaritan woman at the well.

John 4:20-24 [TS]
20 “Our fathers *worshipped on this mountain, but you people say that in Yerushalayim{Jerusalem} is the place where one needs to worship.” 
21 יהושע{Yeshua} said to her, “Woman, believe Me, the hour is coming when you shall neither on this mountain, nor in Yerushalayim, worship the Father. 
22 “You *worship what you do not know. We worship what we know, because the deliverance is of the Yehudim{Jews}
23 “But the hour is coming, and now is, when the true worshippers{proskunetes} shall worship the Father in spirit and truth, for the Father also does seek such to worship Him. 
24 “Elohim is Spirit, and those who worship Him need to worship in spirit and truth.”
*proskuneo = worship (compare also John12:20; Acts7:43; 8:27; 24:11)

These verses should be enough to confirm that «proskuneo» has a wide range of meaning: from deep respect to actual “worship” of the Almighty Eternal. It ought also to be clear from the account of the Samaritan woman that Yeshua teaches that ‘worship’ belongs only to His Elohim and Father. Nowhere does Yeshua ever encourage ‘worship’ of himself.
Indeed, in the temptation account, Yeshua uses both «proskuneo» in combination with «latreuo» regarding the Eternal only.

Matthew 4:9-10 [TS]
9 and said to Him, “All these I shall give You if You fall down and worship me.” 
10 Then יהושע{Yeshua} said to him, “Go, Satan! For it has been written, ‘You shall worship{proskuneo} יהוה your Elohim, and Him alone you shall *serve{latreuo}.
*sacred service

Some, mainly trinitarians, but also others, believe in the worship of the Eternal as well as His Son. Since the pre-existent Son, as well as the glorified Messiah, are referred to by the designation “god” this amounts to the worship of two gods, contradicting historical monotheism of the Jews as well as the early Christians. 

Yeshua never taught the worship of two deities, or the worship of anyone other than his Father, the Eternal. The verses where «proskuneo» appears when applied to Yeshua, mean simply a high degree of honour and respect, not ‘worship’. 
Consider some of those verses below.

Matthew 8:2 [TS]
And see, a leper came, and *bowed before Him{Yeshua}, saying, “Master, if You desire, You are able to make me clean.” 
Matthew 9:18
While He was saying all this to them, see, a ruler came and *bowed down to Him{Yeshua}, saying, “My daughter is dead by now, but come and lay Your hand on her and she shall live.” 
Matthew 14:33
And those in the boat came and did *bow to Him, saying, “Truly You are the Son of Elohim.” 
Matthew 15:25
But she came and was *bowing to Him, saying, “Master, help me!” 
Matthew 20:20
Then the mother of the sons of Zabdai{Zebedee} came to Him with her sons, *bowing down and making a request of Him.
Matthew 28:9 [Israeli Authorised Version - IAV]
And as they went to tell his talmidim{disciples}, behold, Y'shuw'a{Yeshua} met them, saying, All hail. And they came and held him by the feet, and *payed homage to him.
Matthew 28:17
And when they saw Him{Yeshua}, they *bowed to Him, but some doubted.
Mark 5:6 [TS]
 And seeing יהושע{Yeshua} from a distance, he{the demonised man} ran and *bowed down to Him
John 9:38
And he{the blind man} said, “Master, I believe,” and *bowed before Him{Yeshua}.

All of these examples show the deepest respect toward Yeshua but do not indicate worship.

However, there are two texts which seem to show heavenly beings worshipping Yeshua

Hebrews 1:6
 And when He again brings the first-born into the world, He says, “Let all the messengers of Elohim *do reverence to Him.”

When Yeshua was resurrected and thus brought again into the world of the living after three days in the tomb, all of the Eternal’s messengers (generally known as angels) must have bowed and prostrated themselves out of the deepest respect. This is not ‘worship’ in the modern meaning of that word.  This text only shows the reaction of the heavenly hosts to the victory of the Son and no doubt on his presentation in heaven to receive his kingdom, they showed proper respect after the Eastern manner – see Daniel 7:13, 14.

Revelation 5:14
And the four living creatures said, “Amen! And the twenty-four elders fell down and *bowed before Him who lives forever and ever. 

There are many interpretations as to who the four creatures are. Regardless of this, both texts deal with heavenly beings and nowhere are earthly servants enjoined to ‘worship’ Yeshua. «Proskuneo» here may be viewed, not as worship, but of a gesture of deepest respect for both Yahweh Almighty and Yeshua the Lamb.  
Shaul (Paul), in describing the apostasy of some Jews in Scriptural history, writes: 

Romans 1:25 [HRB] 
...(the unrighteous) changed the truth of YAHWEH into the lie, and worshipped and served the created thing more than the Creator, who is blessed forever. Amen.

Since Yeshua was a creation of the Eternal, the firstborn of every creature – Colossians 1:15, the danger of saying one ‘worships’ Yeshua should become clear.

Shaul clearly separates Yahweh Elohim from Yeshua the Messiah in his letter to the Corinthians

1 Corinthians 8:6 [TS]
for us there is one Elohim, the Father, from whom all came and for whom we live, and one Master יהושע{Yeshua} Messiah, through whom all came and through whom we live.

After the last Passover meal with his disciples Yeshua prayed to his Father and said, among other things, the following

John 17:3 [TS]
 “And this is everlasting life, that they should know You, the only true Elohim, and יהושע{Yeshua} Messiah whom You have sent. 

So knowing the Father, the only true Elohim, Yahweh and Yeshua whom He has sent is ‘everlasting life’.
Later on, Yeshua referred to the Eternal as his Elohim (deity or God) when he met Mary Magdalene after his resurrection

John 20:17 [IAV]
Y'shuw'a{Yeshua} saith unto her, Touch me not; for I am not yet ascended to my Father: but go to my brethren, and say unto them, I ascend unto my Father, and your Father; and to my Elohim{God}, and your Elohim{God}.

In Revelation 3:12 Yeshua calls his Father Elohim four times 

Revelation 3:12
Him that overcometh will I make a pillar in the temple of my Elohim, and he shall go no more out: and I will write upon him the name of my Elohim, and the name of the city of my Elohim, which is new Yerushalayim, which cometh down out of heaven from my Elohim: and I will write upon him my new name. 

Can a deity have a deity? Moreover, if Yeshua were a deity how could he be the ‘Servant of the Eternal’? – Matthew 12:15-21
Scripture does not contradict itself and it tells us that there is only one Elohim

Deuteronomy 6:4
“Hear, O Yisra’el: יהוה our Elohim, יהוה is one! 

 Main Source: Mark Heber Miller

The Hebraic Roots Bible is a literal translation of the Scriptures with the sacred name of Yahweh and Yahshua restored and preserved. Congregation of YHWH, Box 832 Carteret NJ 07008

Moffatt New Testament is a translation in modern speech by James Moffatt. The version is highly colloquial, and allows the reader to quickly follow the progress of thought in many passages (especially in the Epistles) where a more literal rendering makes for difficult going.

The Israeli Authorised Version is the KJV Messianically edited and corrected.
‘YY’ is used for the Tetragrammaton (יהוה), so different groups can pronounce The Most Holy Name as they see fit.