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.

By using the method of differential subordinations, we derive some sufficient conditions for strongly starlike functions associated with a linear operator. All these results presented here are sharp.

Argument estimates for certain analytic functions associated with starlike functions of reciprocal order are obtained and special cases of the main results are indicated.

Let M be a complete simply connected manifold which is in addition Gromov hyperbolic, coercive and roughly starlike. For a given harmonic function on M , a local Fatou Theorem and a pointwise criteria of nontangential convergence coming from the density of energy are shown: at almost all points of the boundary, the harmonic function converges non-tangentially if and only if the supremum of the ...

The present paper deals with some geometric classes of analytic functions, such as starlike, convex and bounded turning property in a complex domain. These classes are defined by a new linear operator in the normalized space of analytic functions. The linear operator is introduced by a convolution of Szego function involving parametric coefficients type Laguerre polynomial, with the normalized ...

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.

Making use of the Hurwitz–Lerch Zeta function, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients of complex order denoted by TS b (α, β, γ) and obtain coefficient estimates, extreme points, the radii of close to convexity, starlikeness and convexity and neighbourhood results for the class TS b (α, β, γ). In parti...

"Let $C$ and $S^*$ stand for the classes of convex starlike mapping in $\D$, let $\cc$, $\cs$ denote closures respective hulls. We derive characterizations when convolution mappings $\cc$ is convex, as well starlike. Several terms are given convexity within starlikeness $\cs$. also obtain a correspondence via between $S^*$, correspondences subclasses that have $n$-fold symmetry."

For a function f starlike of order $$\alpha $$ , $$0\leqslant \alpha <1$$ non-constant polynomial Q degree n which is non-vanishing in the unit disc $${\mathbb {D}}$$ and $$\beta >0$$ we consider $$F:{\mathbb {D}}\rightarrow {\mathbb {C}}$$ defined by $$F(z)=f(z) (Q(z))^{\beta /n}$$ find largest value $$r\in (0,1]$$ such that $$r^{-1} F(rz)$$ lies various known subclasses functions as class $$\...