ON A CLASS OF ANALYTIC FUNCTION RELATED TO SCHWARZ LEMMA

In this paper, we plan to introduce the class of the analytic functions called P (b) and to investigate the various properties of the functions belonging this class. The modulus of the second coefficient c(2) in the expansion of f (z) = z+c(2)z(2)+... belonging to the given class will be estimated from above. Also, we estimate a modulus of the second angular derivative of f (z) function at the boundary point alpha with f' (alpha) = 1 - b, b is an element of C, by taking into account their first nonzero two Maclaurin coefficients.