We investigate convolution properties and coefficients estimates for two classes of analytic functions involving theq-derivative operator defined in the open unit disc. Some of our results improve previously known results.

The Miller–Ross-type Poisson distribution is an important model for plenty of real-world applications. In the present analysis, we study and introduce a new class of bi-univalent functions defined by means of Gegenbauer polynomials with a Miller–Ross-type Poisson distribution series. For functions in each of these bi-univalent function classes, we have derived and explored estimates of the Taylor coefficients $\left|a_2\right|$ and $\left|a_3\right|$ and Fekete-Szegö functional problems for functions belonging to these new subclasses.

In this paper, we study Fekete-Szegö Problem for certain subclass of analytic functions with complex order in the open unit disk by applying the q-analogue of Ruscheweyh operator in conjunction with the principle of subordination between analytic functions.

In the present paper, we consider certain classes of bi-univalent Bazilevic functions with bounded boundary rotation involving Salăgeăn linear operator to obtain the estimates of their second and third coefficients. Further, certain special cases are also indicated. Some interesting remarks about the results presented here are also discussed. . .

Using the results of third-order differential subordination, we introduce certain families of admissible functions and discuss some applications of third-order differential subordination for meromorphic functions associated with a linear operator containing a generalized Mittag-Leffler function.