Coefficient Estimates for a Subclass of Meromorphic Multivalent q-Close-to-Convex Functions

By making use of the concept of basic (or q-) calculus, many subclasses of analytic and symmetric q-starlike functions have been defined and studied from different viewpoints and perspectives. In this article, we introduce a new class of meromorphic multivalent close-to-convex functions with the help of a q-differential operator. Furthermore, we investigate some useful properties such as sufficiency criteria, coefficient estimates, distortion theorem, growth theorem, radius of starlikeness, and radius of convexity for this new subclass.

A Study of a Certain Family of Multivalent Functions Associated with Subordination

The aim of this paper is to introduce a certain family of new classes of multivalent functions associated with subordination. The various results obtained here for each of these classes include coefficient estimates radius of convexity, distortion and growth theorem.

Starlike functions associated with the generalized Koebe function

In this paper we study some properties of functions f which are analytic and normalized (i.e. $$f(0)=0=f'(0)-1$$ f ( 0 ) = 0 = f ′ ( 0 ) - 1 ) such that satisfy the following subordination relation $$\begin{aligned} \left( \frac{zf'(z)}{f(z)}-1\right) \prec \frac{z}{(1-pz)(1-qz)}, \end{aligned}$$ z f ′ ( z ) f ( z ) - 1 ≺ z ( 1 - p z ) ( 1 - q z ) , where $$(p,q) \in [-1,1] \times [-1,1]$$ ( p , q ) ∈ [ - 1 , 1 ] × [ - 1 , 1 ] . These types of functions are starlike related to the generalized Koebe function. Some of the features are: radius of starlikeness of order $$\gamma \in [0,1)$$ γ ∈ [ 0 , 1 ) , image of $$f\left( \{z:|z|<r\}\right) $$ f { z : | z | < r } where $$r\in (0,1)$$ r ∈ ( 0 , 1 ) , radius of convexity, estimation of initial and logarithmic coefficients, and Fekete–Szegö problem.

Applications of a New q -Difference Operator in Janowski-Type Meromorphic Convex Functions

The main aim of the present article is the introduction of a new differential operator in q -analogue for meromorphic multivalent functions which are analytic in punctured open unit disc. A subclass of meromorphic multivalent convex functions is defined using this new differential operator in q -analogue. Furthermore, we discuss a number of useful geometric properties for the functions belonging to this class such as sufficiency criteria, coefficient estimates, distortion theorem, growth theorem, radius of starlikeness, and radius of convexity. Also, algebraic property of closure is discussed of functions belonging to this class. Integral representation problem is also proved for these functions.

A new subclass of meromorphic functions with positive coefficients defining by linear operator

In this paper, we introduce and study a new class σ, (α,λ) of meromorphic univalent functions defined in E = {z : z ∊ ℂ and 0 < |z| < 1} = E \ {0}. We obtain coefficient inequalities, distortion theorems, extreme points, closure theorems, radius of convexity estimates and integral operators. Finally, we obtained neighbourhood result for the class σp(γ,λ).

On a subclass of close-to-convex harmonic mappings

In this paper, we introduce a new class of sense preserving harmonic mappings [Formula: see text] in the open unit disk and prove that functions in this class are close-to-convex. We give some basic properties such as coefficient bounds, growth estimates, convolution and determine the radius of convexity for the sections of functions belonging to this family. In addition, we construct certain harmonic univalent polynomials belonging to this family.

Radius problems for univalent functions

This paper considers the following problem: for what value r, {r<1} a function that is univalent in the unit disk {|z|<1} and convex in the disk {|z|<r} becomes starlike in {|z|<1}. The number r is called the radius of convexity sufficient for starlikeness in the class of univalent functions. Several related problems are also considered.

A Class of Harmonic Starlike Functions defined by Multiplier Transformation

We define two new subclasses, $HS(k, \lambda, b, \alpha)$ and \linebreak $\overline{HS}(k, \lambda, b, \alpha)$, of univalent harmonic mappings using multiplier transformation. We obtain a sufficient condition for harmonic univalent functions to be in $HS(k,\lambda,b,\alpha)$ and we prove that this condition is also necessary for the functions in the class $\overline{HS} (k,\lambda,b,\alpha)$. We also obtain extreme points, distortion bounds, convex combination, radius of convexity and Bernandi-Libera-Livingston integral for the functions in the class $\overline{HS}(k,\lambda,b,\alpha)$.

CONVEXITY CONDITION OF THE GENERALIZED BERNATSKY INTEGRAL FOR ONE SUBCLASS OF STAR-LIKE FUNCTIONS

The article carried out a study on the convexity of the Bernatsky integral in the proposition that the function in question belongs to a subclass of star-shaped functions that satisfy certain conditions. For this, the condition of convexity of univalent functions was considered. The geometrical interpretation of the conditions is given, the radius of the convexity of the star-shaped functions is established. The intervals for the parameter are found for which the Bernatsky integral is a convex function in the whole unit circle, in cases where the parameter does not belong to the given interval, the Bernatsky integral will be a convex function in a circle of smaller radius. Three consequences are given in which various cases of convexity of the Bernatsky integral for analytic functions that belong to classes of functions with certain conditions are analyzed. For the considered classes of analytic functions, the radius of convexity of the Bernatsky integral is determined.