In "death of a salesman", Happy's public denial of hi father at all justifed in the way in which Willy has treated his son throughout his life?

This is an interesting question, and the answer depends
upon the perspective.  Happy has been subjugated to the athletic Biff.  Clearly both
parents have focused attention on Biff to the exclusion of Happy.  Happy's adult life
reflects this need for attention in his womanizing ways and his lack of commitment to
anyone or anything.  He still seeks validation as evidenced by his constant assertions
of losing weight and promising to get married.  Thus, it is understandable that Happy
has sought attention elsewhere and even made his presence scarce around his parents'
home.

However, the word 'justified' is very strong, and the
answer would have to be no.  Happy is not justified in denying his father.  First, the
play gives no evidence that Willy denied Happy.  In fact, Willy includes Happy in his
declaration of "my boys" as he contemplates moving to Alaska with Ben and at the
prospect of the Loman Brothers Sporting Goods store.  Happy is never denied; he is just
not the primary focus.

Furthermore, Willy is clearly
sinking into dementia.  He is slipping away from reality and making an unfortunate
situation more pathetic by his oddly timed outbursts at dinner.  Leaving him in this
state to sit babbling on the bathroom floor cannot be justified, even if Happy felt
slighted as a child.