On Certain Classes of Multivalent Functions Involving a Generalized Differential Operator

Abstract

Abstract. Making use of a generalized differential operator we introduce some new subclasses of multivalent analytic functions in the open unit disk and investigate their inclusion relationships. Some integral preserving properties of these subclasses are also discussed.

Sandwich Theorems for Higher-Order Derivatives of P-Valent Functions Involving a Generalized Differential Operator

“…;p (f g) ( 0, p 2 N; n 2 N 0 ) was introduced and studied by Selvaraj et al [21] (see also [7]), and D n ;1 (f g) (z) = D n (f g) (z), where the operator D n (f g) was introduced by Aouf and Mostafa [6];…”

On second-order differential subordinations for a class of analytic functions defined by convolution

“…The operator Q m λ,p (f * g) was introduced and studied by Selveraj and Selvakumaran [19], Aouf and Mostafa [4], and for p = 1 was introduced by Aouf and Mostafa [3]. Recent years,Özkan [16],Özkan and Altntaş [17], Lupaş [9], and Lupaş [10] (also see [1,2]) investigated some applications and results of subordinations of analytic functions given by convolution.…”