Based on a family of bi-univalent functions introduced through the Faber polynomial expansions and Noor integral operator

<abstract><p>In this study, by using $ q $-analogue of Noor integral operator, we present an analytic and bi-univalent functions family in $ \mathfrak{D} $. We also derive upper coefficient bounds and some important inequalities for the functions in this family by using the Faber polynomial expansions. Furthermore, some relevant corollaries are also presented.</p></abstract>

Coefficient bounds for new subclasses of analytic and m-fold symmetric bi-univalent functions

In the present paper, we introduce and study two new subclasses of analytic and $m$-fold symmetric bi-univalent functions defined in the open unit disk $U$. Furthermore, for functions in each of the subclasses introduced here, we obtain upper bounds for the initial coefficients $\left| a_{m+1}\right|$ and $\left| a_{2m+1}\right|$. Also, we indicate certain special cases for our results.

A study of sharp coefficient bounds for a new subfamily of starlike functions

In this article, by employing the hyperbolic tangent function tanhz, a subfamily $\mathcal{S}_{\tanh }^{\ast }$ S tanh ∗ of starlike functions in the open unit disk $\mathbb{D}\subset \mathbb{C}$ D ⊂ C : $$\begin{aligned} \mathbb{D}= \bigl\{ z:z\in \mathbb{C} \text{ and } \vert z \vert < 1 \bigr\} \end{aligned}$$ D = { z : z ∈ C and | z | < 1 } is introduced and investigated. The main contribution of this article includes derivations of sharp inequalities involving the Taylor–Maclaurin coefficients for functions belonging to the class $\mathcal{S}_{\tanh }^{\ast } $ S tanh ∗ of starlike functions in $\mathbb{D}$ D . In particular, the bounds of the first three Taylor–Maclaurin coefficients, the estimates of the Fekete–Szegö type functionals, and the estimates of the second- and third-order Hankel determinants are the main problems that are proposed to be studied here.

Generalized Close-to-Convexity Related with Bounded Boundary Rotation

The class Pα,m[A, B] consists of functions p, analytic in the open unit disc E with p(0) = 1 and satisfy p(z) = (m/4 + ½) p1(z) – (m/4 – 1/2) p2(z), m ≥ 2, and p1, p2 are subordinate to strongly Janowski function (1+Az/1+Bz)α, α ∈ (0, 1] and −1 ≤ B < A ≤ 1. The class Pα,m[A, B] is used to define Vα,m[A, B] and Tα,m[A, B; 0; B1], B1 ∈ [−1, 0). These classes generalize the concept of bounded boundary rotation and strongly close-to-convexity, respectively. In this paper, we study coefficient bounds, radius problem and several other interesting properties of these functions. Special cases and consequences of main results are also deduced.

Coefficient Bounds of Kamali-Type Starlike Functions Related with a Limacon-Shaped Domain

In this article, we familiarize a subclass of Kamali-type starlike functions connected with limacon domain of bean shape. We examine certain initial coefficient bounds and Fekete-Szegö inequalities for the functions in this class. Analogous results have been acquired for the functions f − 1 and ξ / f ξ and also found the upper bound for the second Hankel determinant a 2 a 4 − a 3 2 .

A Certain Subclass of Analytic Functions with Negative Coefficients Defined by Gegenbauer Polynomials

In this paper, we introduce a new subclass of analytic functions with negative coefficients defined by Gegenbauer polynomials. We obtain coefficient bounds, growth and distortion properties, extreme points and radii of starlikeness, convexity and close-to-convexity for functions belonging to the class T S λ m ( γ , e , k , v ) TS_\lambda ^m(\gamma ,e,k,v) . Furthermore, we obtained the Fekete-Szego problem for this class.

Certain Class of Analytic Functions with respect to Symmetric Points Defined by Q-Calculus

In this study, we familiarise a novel class of Janowski-type star-like functions of complex order with regard to j , k -symmetric points based on quantum calculus by subordinating with pedal-shaped regions. We found integral representation theorem and conditions for starlikeness. Furthermore, with regard to j , k -symmetric points, we successfully obtained the coefficient bounds for functions in the newly specified class. We also quantified few applications as special cases which are new (or known).

Coefficient Bounds for Al-Oboudi Type Bi-univalent Functions based on a Modified Sigmoid Activation Function and Horadam Polynomials

Using the Al-Oboudi type operator, we present and investigate two special families of bi-univalent functions in $\mathfrak{D}$, an open unit disc, based on $\phi(s)=\frac{2}{1+e^{-s} },\,s\geq0$, a modified sigmoid activation function (MSAF) and Horadam polynomials. We estimate the initial coefficients bounds for functions of the type $g_{\phi}(z)=z+\sum\limits_{j=2}^{\infty}\phi(s)d_jz^j$ in these families. Continuing the study on the initial cosfficients of these families, we obtain the functional of Fekete-Szeg\"o for each of the two families. Furthermore, we present few interesting observations of the results investigated.

Coefficient bounds for certain families of bi-univalent functions defined by Wanas operator

The main purpose of this paper is to find upper bounds for the second and third Taylor–Maclaurin coefficients for two families of holomorphic and bi-univalent functions associated with Wanas operator. Further, we point out certain special cases for our results.

ON COEFFICIENT BOUNDS AND FUNCTIONALS OF ANALYTIC FUNCTIONS ON A UNIT DISC

We introduce and investigate a new subclasses of the function class of biunivalent functions defined in the open unit disk, which are associated with linear combinations of some geometric expressions, satisfying subordinate conditions. Coefficients and Fekete-Szegö functional for the class are obtained.