Geometric properties of mixed operator involving Ruscheweyh derivative and Salagean operator

Abstract

Operator theory is a magnicent tool for studying the geo-
metric behaviors of analytic functions in the open unit disk. Recently, a
combination between two well known dierential operators, Ruscheweyh
derivative and Salagean operator are suggested by Lupas in [1]. In this
eort, we shall follow the same principle, to formulate a generalized
dierential-dierence operator. We deliver a new class of analytic func-
tions containing the generalized operator. Applications are illustrated in
the sequel concerning some dierential subordinations of the operator.