Coefficient problems of a class of q-starlike functions associated with q-analogue of Al-Oboudi-Al-Qahtani integral operator and nephroid domain

By making use of $q$-derivative and $q$-integral operators, we define a class of analytic and bi-univalent functions in the unit disk $|z|&lt;1$. Subsequently, we investigate some properties such as some early coefficient estimates and then obtain the Fekete-Szeg\"o inequality for both real and complex parameters. Further, some interesting corollaries are discussed. 

Estimates for a Generalized Class of Analytic and Bi-univalent Functions Involving Two q-Operators

In this study, we introduce a new class of normalized analytic and bi-univalent functions denoted by DΣ(δ,η,λ,t,r). These functions are connected to the Bazilevič functions and the λ-pseudo-starlike functions. We employ Sakaguchi Type Functions and Horadam polynomials in our survey. We establish the Fekete-Szegö inequality for the functions in DΣ(δ,η,λ,t,r) and derive upper bounds for the initial Taylor–Maclaurin coefficients |a2| and |a3|. Additionally, we establish connections between our results and previous research papers on this topic.

Applications of Horadam Polynomials for Bazilevič and λ-Pseudo-Starlike Bi-Univalent Functions Associated with Sakaguchi Type Functions

The study carried out in this paper is on a set of analytic-univalent functions whose definition is connected with the applications of the normalized Mathieu-type series, Opoola differential operator, Oyekan-Swamy-Opoola operator and Janowski-type starlike functions. More so, the techniques of convolution and subordination are embraced in the definition of our set of functions. Some of our investigations include the coefficient inequality, radii problems, growth, distortion, closure and inclusion properties.

On a Set of Generalized Janowski-Type Starlike Functions Connected With Mathieu-Type Series and Opoola Differential Operator

The purpose of this paper is to study the coefficient estimates of the class of functions in ()consisting of starlike functions. The sharp upper bounds for the initial coefficients and the Fekete-Szego functional of the functions in the class were established using the Opoola Differential Operator 

pdf/coefficient-estimate-for-a-subclass-ofanalytic-functions-3wnzs41jng.pdf

Coefficient Estimate for a Subclass ofAnalytic Functions Defined by aGeneralizedDifferential Operator

We use the concept of q-differentiation to define a class Eq(β, δ) of analytic and univalent functions. The investigations thereafter includes coefficient estimates, inclusion property and some conditions for membership of some analytic functions to be in the class Eq(β, δ). Our results generalize some known and new ones.

/pdf/some-investigations-on-a-class-of-analytic-and-univalent-26ae2hu4.pdf

Some Investigations on a Class of Analytic and Univalent Functions Involving q-Differentiation


 In this investigation, we introduce a new q-differential operator that generalizes the well-known Opoola differential operator. Using the operator, we define a family of q-bounded turning functions. The new class is denoted by ℛ
 q
 n
 (µ, β, τ ; λ). Afterwards, inclusion, characterisation, growth, distortion, covering, linear combination and neighborhood properties of functions f ∈ ℛ
 q
 n
 (µ, β, τ ; λ) are presented.

Some Properties of a Family of Univalent Functions Defined by a Generalized Opoola Differential Operator

In this work, we investigate the (p, q)-Gegenbauer polynomials for a class of analytic and bi-univalent functions defined in the open unit disk, with respect to subordination. We give an elementary proof to establish some estimates for the coefficient bounds for functions in the new class. We conclude the study by giving a result of the Fekete-Szegö theorem. A corollary was given to show some results of some subclasses of our new class.

/pdf/applications-of-p-q-gegenbauer-polynomials-on-a-family-of-bi-1hw0xfwq.pdf

Applications of (p, q)-Gegenbauer Polynomials on a Family of Bi-univalent Functions

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