Geometric properties of mixed operator involving Ruscheweyh derivative and Salagean operator

Abstract

"Operator theory is a magnificent tool for studying the geometric beha- viors of holomorphic functions in the open unit disk. Recently, a combination bet- ween two well known di erential operators, Ruscheweyh derivative and Salagean operator are suggested by Lupas in [10]. In this effort, we shall follow the same principle, to formulate a generalized di erential-difference operator. We deliver a new class of analytic functions containing the generalized operator. Applications are illustrated in the sequel concerning some di erential subordinations of the operator."