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.

Inthis paper, the main aim is to introduce the class $mathcal{U}_p(lambda,alpha,beta,k_0)$ of $p$-harmonic mappings togetherwith its subclasses $mathcal{U}_p(lambda,alpha,beta,k_0)capmathcal {T}_p$ and $mathcal{U}_p(lambda,alpha,beta,k_0)capmathcal {T}_p^0$, andinvestigate the properties of the mappings in these classes. First,we give a sufficient condition for mappings to be in $mathcal{U}_p(l...

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...

This paper deals with p-valent strongly starlikeness of the class SP (α,A,B) satisfying the subordination e zf ′(z) f(z) ≺ cos z 1 +Az 1 +Bz + i sin α, f ∈ A, z ∈ ∆, 0 ≤ α < 1, −1 ≤ B < A ≤ 1. We are concerned with computing the radius results for the above mentioned class and the results that we obtained are generalizations of earlier results obtained previously by different authors. MSC: 30C4...

Let the functions q1 be analytic and let q2 be analytic univalent in the unit disk. Using the methods of differential subordination and superordination, sufficient conditions involving the Schwarzian derivative of a normalized analytic function f are obtained so that either q1 z ≺ zf ′ z /f z ≺ q2 z or q1 z ≺ 1 zf ′′ z /f ′ z ≺ q2 z . As applications, sufficient conditions are determined relati...

Let for fixed n ∈ N, Σn denotes the class of function of the following form f(z) = 1 z + ∞ ∑ k=n akz , which are analytic in the punctured open unit disk ∆∗ = {z ∈ C : 0 < |z| < 1}. In the present paper we defined and studied an operator in F (z) = [ c+ 1− μ zc+1 ∫ z 0 ( f(t) t )μ tdt ] 1 μ , for f ∈ Σn and c+ 1− μ > 0.