Properties of functions concerned with Caratheodory functions

Abstract

Let Pn denote the class of analytic functions p(z) of the form p(z) = 1+ cnzn + cn+1zn+1 + ... in the open unit disc U. Applying the result by S. S. Miller and P. T. Mocanu (J. Math. Anal. Appl. 65 (1978), 289–305), some interesting properties for p(z) concerned with Carath´eodory functions are discussed. Further, some corollaries of the results concerned with the result due to M. Obradović and S. Owa (Math. Nachr. 140 (1989), 97–102) are shown.