Ar-Rahman (the Most Gracious), Ar-Rahim (the Most Merciful).
We explained these Names in the Basmalah.
Al-Qurtubi said,
"Allah has described Himself by `Ar-Rahman, Ar-Rahim' after saying `the Lord of the Alamin', so His statement here includes a warning, and then an encouragement.
Similarly, Allah said,
نَبِّىءْ عِبَادِى أَنِّى أَنَا الْغَفُورُ الرَّحِيمُ
وَأَنَّ عَذَابِى هُوَ الْعَذَابُ الاٌّلِيمُ
Declare (O Muhammad) unto My servants, that truly, I am the Oft-Forgiving, the Most Merciful. And that My torment is indeed the most painful torment. (15;49-50)
Allah said,
إِنَّ رَبَّكَ سَرِيعُ الْعِقَابِ وَإِنَّهُ لَغَفُورٌ رَّحِيمٌ
Surely, your Lord is swift in retribution, and certainly He is Oft-Forgiving, Most Merciful. (6;165)
Hence, Rabb contains a warning while Ar-Rahman Ar-Rahim encourages.
Further, Muslim recorded in his Sahih that the Messenger of Allah said,
لَوْ يَعْلَمُ الْمُوْمِنُ مَا عِنْدَ اللهِ مِنَ الْعُقُوبَةِ مَا طَمِعَ فِي جَنَّتِهِ أَحَدٌ وَلَوْ يَعْلَمُ الْكَافِرُ مَا عِنْدَ اللهِ مِنَ الرَّحْمَةِ مَا قَنَطَ مِنْ رَحْمَتِهِ أَحَدٌ
If the believer knew what punishment Allah has, none would have hope in acquiring His Paradise, and if the disbeliever knew what mercy Allah has, none will lose hope of earning His earning.
Indicating Sovereignty on the Day of Judgment
Allah said next,
مَـالِكِ يَوْمِ الدِّينِ
(