A SHARP SCHWARZ LEMMA AT THE BOUNDARY

Abstract

In this paper, a boundary version of Schwarz lemma is investigated. For the function holomorphic f(z) = a + c(p)z(P) c(p)+1(zP+1) . . . defined in the unit disc satisfying |f(z) - 1| < 1, where 0 < a < 2, we estimate a module of angular derivative at the boundary point b, f (b) = 2, by taking into account their first nonzero two Maclaurin coefficients. The sharpness of these estimates is also proved.