Abstract We consider three classes of functions defined using the class $${\mathcal {P}}$$ P all analytic $$p(z)=1+cz+\cdots $$ p ( z ) = 1 + c ? ...

the main aim of this paper is to introduce three classes $h^0_{p,q}$, $h^1_{p,q}$ and $th^*_p$ of $p$-harmonic mappings and discuss the properties of mappings in these classes. first, we discuss the starlikeness and convexity of mappings in $h^0_{p,q}$ and $h^1_{p,q}$. then establish the covering theorem for mappings in $h^1_{p,q}$. finally, we determine the extreme points of the class $th^*_{p}$.

In this paper, we introduce and study a new subclass of analytic functions which are defined by means linear operator. Some results connected to coefficient estimates, growth distortion theorems, radii starlikeness, convexity close-to-convexity integral inequalities related the is obtained.

Abstract We introduce the subclass Tj(n, m, γ, α, λ) of analytic functions with negative coefficients defined by generalized Sălăgean operator D λ . Coefficient estimates, some important properties of the class Tj(n, m, γ, α, λ) and distortion theorems are determined. Further, extremal properties and radii of close-to-convexity, starlikeness and convexity of the class Tj(n, m, γ, α, λ) are obta...

Let A denote the class of functions f (z) which are analytic in the open unit disk and normalized by f (0) = f (0) − 1 = 0. In this paper the expression f (z)−1 f (z)/z is studied using differential subordinations and different properties of f (z) z , as well as sufficient conditions for starlikeness and univalence of f (z) ∈ A, are obtained. Also, several open problems are posed. © 2011 Elsevi...

For certain meromorphic p-valent functioun φ andψ, we study a class of functioun f (z) = 1 zp + ∑∞ n=p anz n, (an ≥ 0), defined in the punctured unit disc D, satisfying R ( (f∗φ)(z) (f∗ψ)(z) ) > α (0 ≤ α ≤ 1, z ∈ D) . Coeffiicient etimate disortion theorem and radii of starlikeness and convexity are obtained. Further we consider integral operators associated with functions belonging to the afor...

The main objective of this paper is to establish some sufficient conditions so that a class normalized Mittag–Leffler-type functions satisfies several geometric properties such as starlikeness, convexity, close-to-convexity, and uniform convexity inside the unit disk. Moreover, pre-starlikeness k-uniform are discussed for these functions. Some also derived belong Hardy spaces Hp H∞. Furthermore...