In ancient Greek, the definite article could serve as a possessive pronoun if the context so indicated. A very common variant in the Greek manuscripts underlying the New Testament is places where some manuscripts have a possessive pronoun and some have only the definite article. And usually, the early translations translating the passage would supply a possessive pronoun in their target language, even when their Greek manuscript source text did not have one.

John 19:26

ESV: When Jesus saw his mother and the disciple whom he loved standing nearby, he said to his mother, “Woman, behold, your son!”
NKJV: When Jesus therefore saw His mother, and the disciple whom He loved standing by, He said to His mother, “Woman, behold your son!”

txt τη μητρι𝔓⁶⁶ 𝔓¹²¹vid ℵ B L W it-b,e SBL TH NA28 {\} ‖ τη μητρι αυτου A DS E N 054 𝔐 lat syr TR RP ‖ lac 𝔓⁶⁰ C D 065.  Here is the entire verse 26 from the Robinson-Pierpont majority text:  Ἰησοῦς οὖν ἰδὼν τὴν μητέρα, καὶ τὸν μαθητὴν παρεστῶτα ὃν ἠγάπα, λέγει τῇ μητρὶ αὐτοῦ, Γύναι, ἰδοὺ ὁ υἱός σου.  In ancient Greek the definite article, in this case τη, could serve as a possessive pronoun if the context so indicated.  The addition of the possessive pronoun αυτου, “his,” was not necessary.  All you need to do is look at the beginning of this same verse, where all Greek manuscripts have only την μητερα, the definite article with “mother” and no possessive pronoun present, yet ALL English translations supply the word “his” there.  It is a very common textual variant in the Greek New Testament for Greek manuscripts to add a possessive pronoun like this.  But this need not even be footnoted, as the presence or absence of the possessive pronoun makes no difference in how you would translate it.

Here are some other instances where the Greek texts vary on the presence or absence of the possessive pronoun.  And observe that the English translations all supply an English possessive pronoun no matter which Greek text they translate from:

John 6:52
NKJV: The Jews therefore quarreled among themselves, saying, “How can this Man give us His flesh to eat?”

txt omit 𝔓⁷⁵vid ℵ C D E G H K L M S U W Y Γ Δ Θ Λ Π Ψ Ω 047 0141 0211 ƒ¹ ƒ¹³ 2 28 33 157 180 205 397 565 579 700 1006 1010 1071 1241 1292 1342 1505 l844 l2211 𝔐 Lect it-d,ff² goth Orgr Cyr½ TR RP TH ‖ αυτου 𝔓⁶⁶ B T 597 892 1243 1424 l253 (l1016) it-a,aur,b,c,e,f,j,q,r¹ vg syr-c,s,p,h,pal cop-sa,pbo,bo,ach² arm eth geo slav Or-lat Macarius/Symeon Chrys Cyr½ SBL [NA28] {C} ‖ lac A F N P Q V X 091 0233

John 18:11
ESV: So Jesus said to Peter, “Put your sword into its sheath; shall I not drink the cup that the Father has given me?”
EMTV: So Jesus said to Peter, “Put your sword into its sheath; shall I not drink the cup that the Father has given me?”

txt την μαχαιραν 𝔓⁶⁰ 𝔓⁶⁶ ℵ A B C D E L N W 047 054 𝔐 lat syr RP SBL TH NA28 {\} ‖ την μαχαιραν σου vg-cl Cyr Or TR ‖ lac 𝔓⁷⁵ 𝔓¹⁰⁸.  Almost all the English translations which translate the RP / NA28 text read “your sword.”  (Not ASV, NASB)

John 5:10b
NKJV: The Jews therefore said to him who was cured, “It is the Sabbath; it is not lawful for you to carry your bed.”

txt σου 𝔓⁶⁶ 𝔓⁷⁵ ℵ C* D L N Ws Θ Λ Π Ψ 0211 0233 ƒ¹³ 69 579 892 1071 1241 lat syr cop arm SBL NA28 {/} ‖ omit A B C³ E F G H K M S U V Xsupp Y Γ Δ Ω 047 063 0141 ƒ¹ 2 28 124 157 397 565 700 1424 𝔐 it-e,δ TR RP TH ‖ lac 𝔓⁴⁵ P Q T Xtxt 070 078 33 346 788

Matthew 15:2a χειρας αυτων C D E L N P W Σ Φ 𝔐 lat syr TR RP SBL ΤH NA28 [αυτων] {\} ‖ χειρας ℵ B 073 it-f,g¹ arm Or Cyr Chr ‖ lac A Z 0233 0281.

Matthew 23:5b txt τα κρασπεδα ℵ B D cop-sa,mae¹ eth? SBL TH NA28 {\} ‖ τα κρασπεδα αυτων itb vgmss copsa? eth ‖ τα κρασπεδα των ιματιων L ‖ τα κρασπεδα των ιματιων αυτων E O W Σ 0102 0107 it-f,ff²*,h,q syr arm Bas TR RP ‖ lac A C N P Z Φ 0233 0281.

Luke 23:2 txt το εθνος ημων 𝔓⁷⁵ ℵ B D L N T lat syr SBL TH NA28 {\} ‖ το εθνος A E W 𝔐 it-a,r¹ MarcionE TR RP ‖ lac 𝔓⁴⁵ C P Q.

Mark 3:5a txt την χειρα B E Φ SBL NA28 {\} ‖ την χειρα σου ℵ A C D L P W Σ TR RP TH ‖ lac 𝔓⁴⁵ N 064 072.

Mark 14:46 txt τας χειρας αυτω ℵ² B D L it-(a,k),q syr SBL TH NA28 {\} ‖ τας χειρας αυτων ℵ* C W 0233 ‖ αυτω τας χειρας αυτων N Σ ‖ επ αυτον τας χειρας αυτων E Φ 𝔐 (lat) TR RP ‖ τας χειρας αυτων επ αυτον A ‖ lac 𝔓⁴⁵ P 083.

1 Peter 3:10b txt αυτου L P 049 0142 307 lat-s,v,t cop-sa,bo syr-p arm eth TR AN BG RP ‖ omit 𝔓⁷² 𝔓⁸¹vid ℵ A B C K Ψ 33 623 1175 1243 1735 1739 2464 2805 syr-h geo SBL TH NA28 ‖ lac 𝔓⁷⁴ 048 093 0206 0247 0285 ℓ1575.

2 Peter 2:20 f- κυρίου καὶ σωτῆρος Ἰησοῦ Χριστοῦ B K 049 307 2423 ps-oec it-z lat-v-mss TR AN BG RP SBL ECM2 TH NA28 ‖ a- κυρίου ἡμῶν καὶ σωτῆρος Ἰησοῦ Χριστοῦ 𝔓⁷² ℵ A C P Ψ 048vid 0142 5 33 623 1175 1243 1448 1735 1739 1852 2298 2464 lat-v,t syr-h arm (eth) geo slav pelag aug ECM1 ‖ b- κυρίου ἡμῶν Ἰησοῦ Χριστοῦ καὶ σωτῆρος (ἡμῶν) cop-sa syr-ph-mss ‖ c- κυρίου καὶ σωτῆρος ἡμῶν Ἰησοῦ Χριστοῦ 94 104 syr-ph-mss ‖ d- κυρίου καὶ σωτῆρος ὑμῶν Ἰησοῦ Χριστοῦ 1241 ‖ e- κυρίου ἡμῶν Ἰησοῦ Χριστοῦ L 459 anast-s copbo ‖ g- κυρίου Ἰησοῦ Χριστοῦ 6 2805 ‖ a/c copv ‖ e/g syrphmss ‖ lac 𝔓⁷⁴ 048 0156 0209 0247 665. 

1 John 3:21a txt ἡ καρδία ἡμῶν ℵ C K L 049 056 0142 18 81 88 104 181 326 330 424* 451 614 629 630 1175 1243 1292 1505c 1611 1844 1852 1877 1881 2138 2298 2412 2464 2492 𝔐 Lect it-ar,q,r,t,w,z vg-cl,ww syr-p,h Cllat Orpt Did TR AN BG RP NA28 {C} ‖ ἡ καρδία A B Ψ 33 322 323 424c 436 945 1067 1241 1409 1735 1739 2344 vg-st Orgr⅓,lat2/4 (Methodius); Aug½ SBL TH ‖ ἡ καρδία ὑμῶν 1505* pc ‖ lac 𝔓⁹ 𝔓⁷⁴ P 048 0245 0296.