Some univalence conditions related to a general integral operator

For some classes of analytic functions f, g, h and k in the open unit disk 𝕌, we consider the general integral operator 𝒢_n, that was introduced in a recent work [1] and we obtain new conditions of univalence for this integral operator. The key tools in the proofs of our results are the Pascu’s and the Pescar’s univalence criteria, as well as the Mocanu’s and Şerb’s Lemma. Some corollaries of the main results are also considered. Relevant connections of the results presented here with various other known results are briefly indicated.