Applications of the l ‐Binomial Theorem to Certain Subclasses of Univalent Functions

In this paper, we investigate a binomial theorem associated with the l ‐gamma function. This binomial generalizes both the Pascal operator and the Ruscheweyh differential operator. We establish necessary and sufficient conditions for the l ‐binomial theorem to belong to various subclasses of analytic and univalent functions in the open unit disc. We also study a certain integral operator associated with the l ‐binomial theorem. The results obtained generalize several previously established results in the literature.