A new generalized differential operator and its defined subclass of analytic functions

Abstract

In geometric function theory, differential operators are invaluable in the study of analytic and univalent functions defined in the open unit disk. Several operators have been introduced in the literature, including those of Ruscheweyh, Salagean, Al-Oboudi, and other related generalizations, to develop and study various subclasses of regular functions. In this paper, we introduce a new generalized differential operator which extends the well-known Al-Oboudi operator through the incorporation of the Hurwitz–Lerch zeta function. With this operator, a new subclass of analytic and univalent functions is defined and investigated. Several fundamental properties of this class are established, including necessary and sufficient conditions for membership in the class, characterizations, and integral representation results. The obtained results generalize a number of previously known subclasses associated with earlier differential operators and contribute further developments to the theory of regular functions involving special functions.