Inclusion and Preservation Properties for a Generalized Ruscheweyh–Bernardi Operator

Abstract

A generalized multiplier operator obtained by combining a Ruscheweyh-type convolution transform with the Bernardi integral is introduced for normalized analytic functions in the open unit disk. New subclasses associated with starlike, convex and close-to-convex functions of order alpha are defined through this operator. Several inclusion relations, parameter monotonicity properties and class-preserving results are established. The proofs use coefficient identities, a first-order differential subordination lemma and the commutativity of convolution operators. Special choices of the parameters recover familiar results for the Alexander, Libera and Bernardi transforms.