Abstract In the paper there is considered a generalization of well-known Fekete–Szegö type problem onto some Bavrin’s families complex valued holomorphic functions several variables. The definitions correspond to geometric properties univalent variable, like as starlikeness and convexity. First all, are investigated such which elements satisfy also ( j , k )-symmetry condition. As application t...

In this paper, we investigate the coefficient bound estimates, second Hankel determinant, and Fekete-Szegö inequality for analytic bi-univalent function class, which call Mocanu type bi-starlike functions, related to a shell-shaped region in open unit disk complex plane. Some interesting special cases of results are also discussed.

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 bi-univalent functions defined by means Gegenbauer polynomials with series. For in each these function classes, have derived explored estimates Taylor coefficients a2 a3 Fekete-Szegö functional problems belonging to subclasses.

In the present paper, we consider a subclass of starlike functions G3/2 defined by ratio analytic representations convex and functions. The main aim is to determine bounds Fekete–Szegö-type inequalities Hankel determinants for in this class. It proved that maxH3,1(f):f∈G3/2 equal 181. f∈G3/2 are sharp.

In this paper, we make use of the concept q−calculus in theory univalent functions, to obtain bounds for certain coefficient functional problems Janowski type starlike functions and find Fekete–Szegö functional. A similar results have been done function ℘−1. Further, newly defined class determine estimates, distortion bounds, radius problems, related partial sums.

In this work, we investigate the (p, q)-Gegenbauer polynomials for a class of analytic and bi-univalent functions defined in open unit disk, with respect to subordination. We give an elementary proof establish some estimates coefficient bounds new class. conclude study by giving result Fekete-Szegö theorem. A corollary was given show results subclasses our

Basic properties of probability with Poisson distribution is used in obtaining the coefficient bound by subordination principle which fundamental purpose this work. A class analytic function $f:\xi \rightarrow \mathbb{C}$ unit disc $\xi :\{z\in\mathbb{C}:|z|<1\}$ established. Likewise known results Fekete-Szegö inequalities type and second Toeplitz determinant are obtained.