COEFFICIENT ESTIMATES AND QUASI-SUBORDINATION PROPERTIES ASSOCIATED WITH CERTAIN SUBCLASSES OF ANALYTIC AND BI-UNIVALENT FUNCTIONS

In the present paper, we obtain the estimates on initial coefficients of normalized analytic function f in the open unit disk with f and its inverse g = f(-1) satisfying the conditions that zf'(z)/f(z) and zg'(z)/g(z) are both quasi-subordinate to a univalent function whose range is symmetric with respect to the real axis. Several related classes of functions are also considered, and connections to earlier known results are established. (C) 2015 Mathematical Institute Slovak Academy of Sciences