Making use of Horadam polynomials, we propose a special family of regular functions of the type g z = z + ∑ j = 2 ∞ d j z j which are bi-univalent (or bi-schlicht) in the disc z ∈ ℂ : z < 1 . We find estimates on the coefficients d 2 and d 3 and the functional of Fekete–Szegö for functions in this subfamily. Relevant connections to existing results and new observations of the main result are also presented.

In this paper, we define two classes of meromorphic multivalent functions in the punctured disc U*=w∈C:0<|w|<1 by using the principle of subordination. We investigate a number of useful results including subordination results, some connections with a certain integral operator, sandwich properties, an inclusion relationship, and Fekete-Szegö inequalities for the functions belonging these classes. Our results are connected with those in several earlier works, which are related to this field of Geometric Function Theory (GFT) of Complex Analysis.

<abstract> <p>In this paper, making use of the $ q $-analogue of Carlson-Shaffer operator $ L_{q}\left(a, c\right) $ we introduce a new subclass of spiral-like functions and discuss some subordination results and Fekete-Szego problem for this generalized function class. Further, some known and new results which follow as special cases of our results are also mentioned.</p> </abstract>

The prime purpose of this article is to derive a necessary and sufficient condition for a linear operator associated with the Pascal distribution series to be in the class T S μ , σ , δ of analytic functions. Moreover, inclusion relation and an integral operator linked to the Pascal distribution series is considered. We have also provided some results as corollaries of our theorems.