Subordination And Convolution Of Multivalent Functions And Starlikeness Of Integral Transforms - Badghaish, Abeer Omar (2012)
This thesis deals with analytic functions as well as multivalent functions de- ned on the unit disk U. In most cases, these functions are assumed to be normalized, either of the form f(z) = z + 1X k=2 akzk; or f(z) = zp + 1X k=1 ak+pzk+p; p a xed positive integer. Let A be the class of functions f with the rst normalization, while Ap consists of functions f with the latter normalization. Five research problems are discussed in this work. First, let f(q) denote the q-th derivative of a function f 2 Ap. Using the theory of dierential subordination, sucient conditions are obtained for the following dierential chain to hold: f(q)(z) (p; q)zp