Meromorphic harmonic univalent functions related with generalized (p,q)-post quantum calculus operators

Extreme Points and Minimal Outer Area Problem for Meromorphic Univalent Functions

In this present paper, we introduced and characterized a new class of meromorphic univalent functions associated with polylogarithm by investigating; coefficient inequality, convolutions property, integral means and other properties of the class.

We prove that the Nevanlinna five-point-theorem on the uniqueness of meromorphic functions is valid for five small meromorphic functions.

To consolidate or adapt to many studies on meromorphic functions, we define a new subclass of meromorphic functions of complex order involving a differential operator. The defined function class combines the concept of spiral-like functions with other studies pertaining to subclasses of multivalent meromorphic functions. Inclusion relations, integral representation, geometrical interpretation, coefficient estimates and solution to the Fekete-Szegö problem of the defined classes are the highlights of this present study. Further to keep up with the present direction of research, we extend the study using quantum calculus. Applications of our main results are given as corollaries.

The purpose of the present paper is to introduce a new subclass of harmonic univalent functions associated with a $q$-Ruscheweyh derivative operator. A necessary and sufficient convolution condition for the functions to be in this class is obtained. Using this necessary and sufficient coefficient condition, results based on the extreme points, convexity and compactness for this class are also obtained.

Many diverse subclasses of analytic functions, q-starlike functions, and symmetric q-starlike functions have been studied and analyzed by using q-analogous values of integral and derivative operators. In this paper, we define a q-analogous value of differential operators for harmonic functions with the help of basic concepts of quantum (q-) calculus operator theory; and introduce a new subclass of harmonic functions associated with the Janowski and q-Mittag–Leffler functions. We obtain several useful properties of the new class, such as necessary and sufficient conditions, criteria for analyticity, compactness, convexity, extreme points, radii of starlikeness, radii of convexity, distortion bounds, and integral mean inequality. Furthermore, we discuss some applications of this study in the form of some results and examples and highlight some known corollaries for verifying our main results presented in this investigation. Finally, the conclusion section summarizes the fact about the (p,q)-variations.

We introduce new classes of meromorphic harmonic univalent functions. Using the duality principle, we obtain the duals of such classes of functions leading to coefficient bounds, extreme points and some applications for these functions.

On uniqueness of Meromorphic functions with shared-sets in an angular domain

We introduce and study a subclass of meromorphic univalent functions with positive coefficients defined by a novel operator and obtain coefficient estimates, closure theorems, convolution properties, partial sums, and δ- neighborhood for the class .

Complex valued harmonic functions that are univalent and sense preserving in the unit disk U can be written in the form f = h + g ,w hereh and g are analytic in U. In this paper, we introduce a class HP(α), (α 0) of functions which are harmonic in U. We give sufficient coefficient conditions for normalized harmonic functions in HP(α). These conditions are also shown to be necessary when the coefficients are negative. This leads to distortion bounds and extreme points.

In this paper, using Differential operator a certain subclass of harmonic univalent functions in the unit disc U = {z ∈ C : |z| < 1} is investigated. Some properties such as coefficient bounds, convex combination, extreme points and convolution conditions of this class are obtained. The newly introduced subclass of harmonic univalent functions is more general than the subclasses earlier found in the literature.

We investigate some properties of a new subclass of harmonic univalent functions defined by multiplier transformation. We obtain coefficient conditions, extreme points, distortion bounds, convolution, and convex combination for the above subclass of harmonic functions.

In this work, using the differential operator and the concept of meromorephic analytic functions we introduce and investigate the class , of functions of the form , which are analytic and meromorphic univalent in the punctured unit disk , satisfying . Further, coefficient bounds, Hadamard product, radius of close to-convexity, inclusive properties and neighbourhoods of functions in our class are obtain.

In this article, we consider meromorphic univalent functions f in the unit disc of the complex plane having a simple pole at z = α ∈ (0, 1) with nonzero residue b at z = α. In 1969, P.N. Chichra proved an area theorem for such functions. In this note, we generalize this theorem and prove an interesting consequence of this result.

We consider the integral means for the class of functions which are meromorphic and univalent in an annulus.