1. `Uthman ibn Hakim al-Ansari said: "I asked Sa`eed ibn Jubayr about fasting in Rajab, and we were then passing through the month of Rajab, whereupon he said: "I heard Ibn `Abbas saying: "The Messenger of Allah used to observe fast so continuously that we thought he would not break it, and did not observe it so continuously that we thought he would not observe fast." Muslim and Abu Dawud relate it in Kitab al-sawm, respectively in the chapter on fasting at times other than Ramadan, and in the chapter of fasting during Rajab.
Imam Nawawi says: "It would appear that the meaning inferred by Sa`eed ibn Jubayr from Ibn `Abbas's report is that fasting in Rajab is is neither forbidden nor considered praiseworthy in itself, rather, the ruling concerning it is the same as the rest of the months. Neither prohibition not praiseworthiness has been established for the month of Rajab in itself, however, the principle concerning fasting is that it is praiseworthy in itself, and in the Sunan of Abu Dawud(*) the Prophet has made the fasting of the sacred months praiseworthy, and Rajab is one of them. And Allah knows best." Sharh Sahih Muslim Kitab 13 Bab 34 #179.
(*) Kitab al-siyam, Chapter: "Fasting During the Sacred Months". Also in Ibn Majah and Ahmad, hadith of the man who repeats: "I can bear more," and to whom the Prophet finally says: "Fast during the sacred months."
It is established that Ibn `Umar fasted during the sacred months: Musannaf `Abd al-Razzaq 4:293, Musannaf Ibn Abi Shayba 1:125.
2. Abdullah, the freed slave of Asma' the daughter of Abu Bakr, the maternal uncle of the son of `Ata', reported: "Asma' sent me to Abdullah ibn `Umar saying: "The news has reached me that you prohibit the use of three things: the striped robe, saddle cloth made of red silk, and fasting the whole month of Rajab." Abdullah said to me: "So far as what you say about fasting in the month of Rajab, how about one who observes continuous fasting? And so far as what you say about the striped garment, I heard `Umar ibn al-Khattab say that he had heard from Allah's Messenger : "He who wears a silk garment, has no share for him (in the Hereafter)." And I am afraid that stripes were part of it. And so far as the red saddle cloth is concerned, here is Abdullah's saddle cloth [=his] and it is red. I went back to Asma' and informed her, so she said: "Here is the cloak (jubba) of Allah's Messenger ," and she brought out to me that cloak made of Persian cloth with a hem of (silk) brocade, and its sleeves bordered with (silk) brocade, and said: "This was Allah's Messenger's cloak with `A'isha until she died, then I got possession of it. The Apostle of Allah used to wear that, and we washed it for the sick so that they could seek cure thereby."" Muslim relates in the first chapter of Kitab al-libas.
Nawawi says: "`Umar's reply concerning fasting in Rajab is a denial on his part of what Asma' had heard with regard to his forbidding it, and it is an affirmation that he fasted Rajab in its entirety as well as fasting permanently, i.e. except the days of `Id and tashreeq. This is his madhhab and the madhhab of his father `Umar ibn al-Khattab, `A'isha, Abu Talha, and others of the Salaf as well as Shafi`i and other scholars. Their position is that perpetual fasting is not disliked (makruh)."
[Another opinion is reported from Ibn `Umar through a hadith from Ahmad reported in "al-Mughni" 3:167 whereby he disliked that people fast the whole of Rajab but said: "Fast some of it and break fast in some of it."]