Communications of the
Korean Mathematical Society CKMS

In this paper, we use higher order derivatives with regard to symmetric points to introduce a class of multivalent starlike functions. The major deviation is that we define some differential characterizations that are subordinate to a function whose real part is not greater than zero. The primary outcomes of this study are initial coefficients and the Fekete-Szeg\H{o} inequality for functions falling under the given class. Also, we have obtained an interesting subordination results involving symmetric functions. The results obtained here extend or unify the various other well-known and new results.

Keywords: Analytic function, convex function, starlike function, Fekete-Szeg\H{o} problem, differential subordination

MSC numbers: Primary 30C45