Certain Classes Of Analytic Functions Research Articles

Certain classes of analytic functions defined by polylogarithm functions

Certain classes of analytic functions defined by polylogarithm functions

Sufficient Conditions for Linear Operators Related to Confluent Hypergeometric Function and Generalized Bessel Function of the First Kind to Belong to a Certain Class of Analytic Functions

Geometric function theory has extensively explored the geometric characteristics of analytic functions within symmetric domains. This study analyzes the geometric properties of a specific class of analytic functions employing confluent hypergeometric functions and generalized Bessel functions of the first kind. Specific constraints are imposed on the parameters to ensure the inclusion of the confluent hypergeometric function within the analytic function class. The coefficient bound of the class is used to determine the inclusion properties of integral operators involving generalized Bessel functions of the first kind. Different results are observed for these operators, depending on the specific values of the parameters. The results presented here include some previously published findings as special cases.

Certain class of analytic functions defined by q-analogue of Ruscheweyh differential operator

In this paper, we obtain coefficient estimates, distortion theorems, radii of close-to-convexity, starlikeness and convexity for functions belonging to the class of analytic starlike and convex functions defined by q−analogue of Ruscheweyh differential operator. Also we find closure theorems, Nk,q,δ (e, g) neighborhood and partial sums for functions in this class. Mathematics Subject Classification (2010): 30C45. Received 07 June 2020; Accepted 06 August 2020

On generalized close-to-convexity related with strongly Janowski functions

"Strongly Janowski functions are used to define certain classes of analytic functions which generalize the concepts of close-to-convexity and bounded boundary rotation. Coefficient results, a necessary condition, distortion bounds, Hankel determinant problem and several other interesting properties of these classes are studied. Some significant well-known results are derived as special cases. Keywords: Starlike, convex, bounded boundary rotation, Carathéodory and Janowski functions, subordination, convolution."

Radius problems for certain classes of analytic functions

"Radius constants for functions in three classes of analytic functions to be a starlike function of order α, parabolic starlike function, starlike function associated with lemniscate of Bernoulli, exponential function, cardioid, sine function, lune, a particular rational function, and reverse lemniscate are obtained. One of these classes are characterized by the condition Re g/(zez ) > 0. The other two classes are defined by using the function g and they consist respectively of functions f satisfying Re f/g > 0 and |f/g − 1| < 1. Keywords: Starlike function, radius of starlikeness, exponential function."

Properties of Certain Subclasses of P-valent Functions Defined by Certain Integral Operator

In this paper, we introduce standard definitions for new subclasses of uniformly starlike, uniformly convex p-valent functions, and study properties some of uniformly certain classes of analytic functions defined by certain integral operator.

Certain classes of analytic Functions involving multiplier transformations by using q-calculus operators

In this paper we define the classes using Janowski class, multiplier transformations and q-calculus. The results investigated for these classes of functions include the co-efficient estimates, inclusion relations, distortion bounds. Extreme points and many more properties.

Majorization property for certain classes of analytic functions associated with general operator

In this study, we introduce two new classes $S_{k}[E, F;\mu; \gamma]$ and $T_{k}(\theta,\,\mu,\,\gamma)$ of analytic functions using the general integral operator. For these two classes, we study the majorization properties. Some applications of the results are discussed in the form of corollaries.

Geometric Properties of Certain Classes of Analytic Functions with Respect to (x,y)-Symmetric Points

In this article, the present study employs the utilization of the concepts pertaining to (x,y)-symmetrical functions, Janowski type functions, and q-calculus in order to establish a novel subclass within the open unit disk. Specifically, we delve into the examination of convolution properties, which serve as a tool for investigating and inferring adequate and equivalent conditions. Moreover, we also explore specific characteristics of the class S˜qx,y(α,β,λ), thereby further scrutinizing the convolution properties of these newly defined classes.

On the Approximation by Mellin Transform of the Riemann Zeta-Function

This paper is devoted to the approximation of a certain class of analytic functions by shifts Z(s+iτ), τ∈R, of the modified Mellin transform Z(s) of the square of the Riemann zeta-function ζ(1/2+it). More precisely, we prove the existence of a closed non-empty set F such that there are infinitely many shifts Z(s+iτ), which approximate a given analytic function from F with a given accuracy. In the proof, the weak convergence of measures in the space of analytic functions is applied. Then, the set F coincides with the support of a limit measure.

On the Discrete Approximation by the Mellin Transform of the Riemann Zeta-Function

In the paper, it is obtained that there are infinite discrete shifts Ξ(s+ikh), h>0, k∈N0 of the Mellin transform Ξ(s) of the square of the Riemann zeta-function, approximating a certain class of analytic functions. For the proof, a probabilistic approach based on weak convergence of probability measures in the space of analytic functions is applied.

Univalence and Starlikeness of Certain Classes of Analytic Functions

For the analytic functions ϕ(ζ)=ζ+∑k=n∞ϕkζk in the unit disk O, we calculate the values of n and α, where the condition ℜ1+ζϕ″(ζ)/ϕ′(ζ)>−α or ℜ1+ζϕ″(ζ)/ϕ′(ζ)<1+α/2 yields univalence and starlikeness. Conditions imply ϕ in the class where all normalized analytic functions U, with ζ/ϕ(ζ)2ϕ′(ζ)−1<1 are obtained. Recent findings are gained, and unique cases are demonstrated. The generalization of the Jack lemma serves the proof of the main result and that our methodology is based on the idea of subordination.

A Certain Class of Analytic Functions Associated with Beta Negative Binomial Distribution Defined on Complex Hilbert Space

In this work , we show and research a new class of univalent and analytic functions with negative coefficients linked to the beta negative binomial distribution on a complicated Hilbert space. We find fascinating geometric features such as the convex set, coefficient estimates, distortion and growth theorems, starlikeness and convexity radii, and describe the extreme points for functions in this class.

On q-Calculus Related Generalization of Close-to-Convexity

We introduce and study $q$-analogue of certain classes of analytic functions which are related with generalized close-to-convexity. Distortion, inclusion results and growth rate of coefficient problem are investigated for these classes. Some applications of our results are highlighted.

On a class of difference operator and its applications to a family of analytic functions

This paper mainly considers the problem of generalizing a certain class of analytic functions by means of a class of difference operators. We consider some relations between starlike or convex functions and functions belonging to such classes. Some other useful properties of these classes are also considered.

The Fekete-Szegö functional and the Hankel determinant for a certain class of analytic functions involving the Hohlov operator

<abstract><p>In this paper, we introduce and study a new subclass of normalized functions that are analytic and univalent in the open unit disk $ \mathbb{U} = \{z:z\in \mathcal{C}\; \; \text{and}\; \; |z| < 1\}, $ which satisfies the following geometric criterion:</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} \Re\left(\frac{\mathcal{L}_{u, v}^{w}f(z)}{z}(1-e^{-2i\phi}\mu^2z^2)e^{i\phi}\right)>0, \end{equation*} $\end{document} </tex-math></disp-formula></p> <p>where $ z\in \mathbb{U} $, $ 0\leqq \mu\leqq 1 $ and $ \phi\in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) $, and which is associated with the Hohlov operator $ \mathcal{L}_{u, v}^{w} $. For functions in this class, the coefficient bounds, as well as upper estimates for the Fekete-Szegö functional and the Hankel determinant, are investigated.</p></abstract>

Geometric Properties for a New Class of Analytic Functions Defined by a Certain Operator

The aim of this paper is to define and explore a certain class of analytic functions involving the (p,q)-Wanas operator related to the Janowski functions. We discuss geometric properties, growth and distortion bounds, necessary and sufficient conditions, the Fekete–Szegö problem, partial sums, and convex combinations for the newly defined class. We solve the Fekete–Szegö problem related to the convolution product and discuss applications to probability distribution.

Necessary and Sufficient Conditions for Normalized Wright Functions to Be in Certain Classes of Analytic Functions

In this paper, the function classes SPp(σ,ν) and UCSP(σ,ν) are investigated for the normalized Wright functions. More precisely, several sufficient and necessary conditions are provided so that the aforementioned functions are in these classes. Furthermore, several corollaries will follow from our results.

Results on a certain class of analytic functions associated with Chebyshev polynomial

In this work, it was established that Chebyshev polynomial of the second kind belongs to the class of functions with positive real part. The convolution of the Chebyshev polynomial and modified sigmoid function was established to also give functions which belong to the class of functions with positive real part. Further more, subordination principle was used to establish new classes of functions. The coefficient bounds for the new classes of functions defined in the work were obtained.

Majorization for Certain Classes of Analytic Functions Defined by Fournier–Ruscheweyh Integral Operator

In this paper, we introduce three new classes S k a M , N ; μ , R k a μ , and T k a θ of analytic functions defined by Fournier–Ruscheweyh integral operator. For these classes, we investigate the majorization problem. Furthermore, a number of new results are shown to follow upon specializing the parameters involved in our main results.