Sufficient conditions for strongly Carath\'eodory functions

Applying the subordination principle for analytic functions in the open unit disk U, I. H. Kim and N. E. Cho (Comput. Math. Appl. 59(2010), 2067-2073) considered some sufficient conditions for Carath'eodory functions. The purpose of this paper is to discuss some sufficient conditions for the class of strongly Carath'eodory functions in U.