Coefficient Inequalities Research Articles

New Applications of the Sălăgean Quantum Differential Operator for New Subclasses of q-Starlike and q-Convex Functions Associated with the Cardioid Domain

In this paper, we define a new family of q-starlike and q-convex functions related to the cardioid domain utilizing the ideas of subordination and the Sălăgean quantum differential operator. The primary contribution of this article is the derivation of a sharp inequality for the newly established subclasses of q-starlike and q-convex functions in the open unit disc U. For this novel family, bounds of the first two Taylor–Maclaurin coefficients, the Fekete–Szegö-type functional, and coefficient inequalities are studied. Furthermore, we also investigate some new results for the inverse function belonging to the classes of q-starlike and q-convex functions. The results presented in this article are sharp. To draw connections between the early and present findings, several well-known corollaries are also highlighted. Symmetric quantum calculus operator theory can be used to investigate the symmetry properties of this new family of functions.

Logarithmic Coefficients Inequality for the Family of Functions Convex in One Direction

The logarithmic coefficients play an important role for different estimates in the theory of univalent functions. Due to the significance of the recent studies about the logarithmic coefficients, the problem of obtaining the sharp bounds for the modulus of these coefficients has received attention. In this research, we obtain sharp bounds of the inequality involving the logarithmic coefficients for the functions of the well-known class G and investigate a majorization problem for the functions belonging to this family. To prove our main results, we use the Briot–Bouquet differential subordination obtained by J.A. Antonino and S.S. Miller and the result of T.J. Suffridge connected to the Alexander integral. Combining these results, we give sharp inequalities for two types of sums involving the modules of the logarithmical coefficients of the functions of the class G indicating also the extremal function. In addition, we prove an inequality for the modulus of the derivative of two majorized functions of the class G, followed by an application.

Sharp Coefficient Bounds for a New Subclass of Starlike Functions of Complex Order γ Associated with Cardioid Domain

In this study, by using the concepts of subordination, we define a new family RM,N,λ,γ of starlike functions of complex order γ connected with the cardioid domain. The main contribution of this article consists of the derivations of sharp inequality, considering the functions belonging to the family RM,N,λ,γ of starlike functions in U. Particularly, sharp bounds of the first two Taylor–Maclaurin coefficients, sharp estimates of the Fekete–Szegö-type functionals, and coefficient inequalities are investigated for this newly defined family RM,N,λ,γ of starlike functions. Furthermore, for the inverse function and the logg(z)z function, we investigate the same types of problems. Several well-known corollaries are also highlighted to show the connections between prior research and the new findings.

Pascu-Rønning Type Meromorphic Functions Based on Sălăgean-Erdély–Kober Operator

In the present investigation, we introduce a new class of meromorphic functions defined in the punctured unit disk Δ*:={ϑ∈C:0<|ϑ|<1} by making use of the Erdély–Kober operator Iς,ϱτ,κ which unifies well-known classes of the meromorphic uniformly convex function with positive coefficients. Coefficient inequalities, growth and distortion inequalities, in addition to closure properties are acquired. We also set up a few outcomes concerning convolution and the partial sums of meromorphic functions in this new class. We additionally state some new subclasses and its characteristic houses through specializing the parameters that are new and no longer studied in association with the Erdély–Kober operator thus far.

Certain results on a class of analytic functions involving q-hypergeometric series

Based on [Formula: see text]-Hypergeometric Series, a linear operator [Formula: see text] is considered and involving this operator a class [Formula: see text] of analytic functions is defined by using [Formula: see text]-derivatives. As a special case, a class [Formula: see text] by involving [Formula: see text]-analogue of Hohlov operator [Formula: see text] is defined. Coefficient inequality for a function [Formula: see text] to be in the class [Formula: see text] is obtained. Further, in terms of subordination, an equivalent condition for a function [Formula: see text] to be in this class is given and using this equivalent class condition results on coefficient estimates including Fekete–Szegö inequality and a convolution result are obtained.

Graded filtrations and ideals of reduction number 2

AbstractIn this paper, we give a way to construct graded filtrations of graded modules. We then apply it to the Sally module, which describes a correction term of the Hilbert function. As a result, we obtain the inequality of the Hilbert coefficients for ideals of reduction number 2 or 3.

CERTAIN SUBCLASSES OF MEROMORPHICALLY P-VALENT FUNCTIONS WITH POSITVE OR NEGATIVE COEFICIENTS USING DIFFERENTIAL OPERATOR

In this paper, we have introduced two subclasses and of meromorphically p-valent functions with positive and negative coefficients, defined by differential operator in the punctured unit disk and obtain some sharp results including coefficient inequality, distortion theorem, radii of starlikeness and convexity, closure theorems of these subclasses of meromorphically p-valent functions. We also derive some interesting results for the Hadamard products of functions belonging to the classes and .

Certain Subclasses of Meromorphic Functions with Positive Coefficients Associated with Linear Operator

In this paper, we introduce and study certain subclass of meromorphic univalent functions by using a linear operator by means of a Hadamard product involving some suitably normalized meromorphically q-Hypergeometric functions, in the punctured open unit disk. Some properties like, coefficients inequalities, growth and distortion theorems, closure theorems, Extreme Points and Radii of meromorphic starlikeness and meromorphic convexity are obtained.

Some new applications of the quantum-difference operator on subclasses of multivalent $ q $-starlike and $ q $-convex functions associated with the Cardioid domain

<abstract><p>In this study, we consider the quantum difference operator to define new subclasses of multivalent $ q $-starlike and $ q $-convex functions associated with the cardioid domain. We investigate a number of interesting problems for functions that belong to these newly defined classes, such as bounds for the first two Taylor-Maclaurin coefficients, estimates for the Fekete-Szeg ö type functional, and coefficient inequalities. The important point of this article is that all the bounds that we have investigated are sharp. Many well-known corollaries are also presented to demonstrate the relationship between prior studies and the results of this article.</p></abstract>

Geometric properties of holomorphic functions involving generalized distribution with bell number

<abstract><p>One of the statistical tools used in geometric function theory is the generalized distribution which has recently gained popularity due to its use in solving practical issues. In this work, we obtained a new subclass of holomorphic functions, which defined by the convolution of generalized distribution and incomplete beta function associated with subordination in terms of the bell number. Further, we estimate the coefficient inequality and upper bound for a subclass of holomorphic functions. Our findings show a clear relationship between statistical theory and geometric function theory.</p></abstract>

Certain differential subordination results for univalent functions associated with $ q $-Salagean operators

<abstract><p>In this paper, we employ the concept of the $ q $-derivative to derive certain differential and integral operators, $ D_{q, \lambda}^{n} $ and $ I_{q, \lambda}^{n} $, resp., to generalize the class of Salagean operators over the set of univalent functions. By means of the new operators, we establish the subclasses $ M^n_{q, \lambda} $ and $ D^n_{q, \lambda} $ of analytic functions on an open unit disc. Further, we study coefficient inequalities for each function in the given classes. Over and above, we derive some properties and characteristics of the set of differential subordinations by following specific techniques. In addition, we study the general properties of $ D_{q, \lambda}^{n} $ and $ I_{q, \lambda}^{n} $ and obtain some interesting differential subordination results. Several results are also derived in some details.</p></abstract>

An application of Pascal distribution involving Kamali type related to leaf like domain

<abstract><p>This paper aims to study the Geometric properties of analytic function in the open unit disk. In the present investigation, we obtain some geometric properties of Pascal distribution involving Kamali type related to leaf like domain. In this paper, we find coefficient inequality, Radii Properties, convolution product, partial sum of the class $ \Sigma(\delta, \Phi, \beta, s, t, m) $. Furthermore, we examine the distortion bounds belonging to the same class.</p></abstract>

On a new subclass of biunivalent functions associated with the $(p,q)$-Lucas polynomials and bi-Bazilevic type functions of order $\rho+i\xi$

Using $ (p, q) $-Lucas polynomials and bi-Bazilevic type functions of order $\rho +i\xi,$ we defined a new subclass of biunivalent functions. We obtained coefficient inequalities for functions belonging to the new subclass. In addition to these results, the upper bound for the Fekete-Szegö functional was obtained. Finally, for some special values of parameters, several corollaries were presented.

On a class of \(p\)-valent functions with negative coefficients defined by opoola differential operator

Using Opoola differential operator, we defined a subclass \(S^{n}_{p}(\lambda,\alpha,\gamma,\delta)\ ) of the class of multivalent or \(p\)-valent functions.Several properties of the class were studied, such as coefficient inequalities,Hadamard product, radii of close-to-convex, star-likeness, convexity, extreme points, the integral mean inequalities for the fractional derivatives, and further growth and distortion theorem are given using fractional calculus techniques.

(U; V )-Lucas polynomial coefficient relations of the bi-univalent function class

In geometric function theory, Lucas polynomials and other special polynomials have recently gained importance. In this study, we develop a new family of bi-univalent functions. Also we examined coefficient inequalities and Fekete-Szegö problem for this new family via these polynomials.

CERTAIN SUBCLASS OF BI-UNIVALENT FUNCTIONS RELATED TO HORADAM POLYNOMIALS ASSOCIATED WITH q-DERIVATIVE

In this paper, by making use of q-derivative, we define a new subclass of analytic and bi-univalent functions related to Horadam polynomials. For func- tions belonging to this class, we derive coefficient inequalities and the Fekete-Szego¨ inequalities. We also provide relevant connections of our results with those consid- ered in earlier investigations

CERTAIN COEFFICIENT INEQUALITIES FOR THE CLASSES OF q-STARLIKE AND q-CONVEX FUNCTIONS

In this paper we determine certain coefficient inequalities for the classes of q-starlike and q-convex function and find the sufficient conditions for generalized Bessel function to belonging in these classes.

On a Certain Subclass of p-Valent Analytic Functions Involving q-Difference Operator

This paper introduces and studies a new class of analytic p-valent functions in the open symmetric unit disc involving the Sălăgean-type q-difference operator. Furthermore, we present several interesting subordination results, coefficient inequalities, fractional q-calculus applications, and distortion theorems.

Coefficient Inequalities for Biholomorphic Mappings on the Unit Ball of a Complex Banach Space

In the first part of this paper, we give generalizations of the Fekete–Szegö inequalities for quasiconvex mappings F of type B and the first elements F of g-Loewner chains on the unit ball of a complex Banach space, recently obtained by H. Hamada, G. Kohr and M. Kohr. We obtain the Fekete–Szegö inequalities using the norm under the restrictions on the second and third order terms of the homogeneous polynomial expansions of the mappings F. In the second part of this paper, we give the estimation of the difference of the moduli of successive coefficients for the first elements of g-Loewner chains on the unit disc. We also give the estimation of the difference of the moduli of successive coefficients for the first elements F of g-Loewner chains on the unit ball of a complex Banach space under the restrictions on the second and third order terms of the homogeneous polynomial expansions of the mappings F.

Coefficient inequalities for a subclass of analytic functions associated with exponential function

Abstract This paper is concerned with the upper bound of various coefficient functionals for a certain subclass of analytic functions associated with exponential function in the open unit disc E = {z ∈ℂ : |z| < 1}. This investigation will motivate other researchers to work in this direction.