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

AbstractIn this article, by employing the hyperbolic tangent function tanhz, a subfamily$\mathcal{S}_{\tanh }^{\ast }$Stanh∗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$\mathcal{S}_{\tanh }^{\ast }$Stanh∗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

Hankel determinants of second and third order for the class S of univalent functions

In this paper we give the upper bounds of the Hankel determinants of the second and third order for the class S of univalent functions in the unit disc

ZALCMAN CONJECTURE AND HANKEL DETERMINANT OF ORDER THREE FOR STARLIKE AND CONVEX FUNCTIONS ASSOCIATED WITH SHELL-LIKE CURVES

The aim of this article is to estimate an upper bound of |_3(1)|, the Zalcman coefficient functional for = 3 and = 4, and also to investigate the fifth, sixth, seventh coefficients of starlike and convex functions associated with shell-like curves. Similar type of outcomes are estimated for the functions ^(−1) and /()

New Developments in Geometric Function Theory

The book contains papers published in a Special Issue of Axioms, entitled "New Developments in Geometric Function Theory". An Editorial describes the 14 papers devoted to the study of complex-valued functions which present new outcomes related to special classes of univalent and bi-univalent functions, new operators and special functions associated with differential subordination and superordination theories, fractional calculus, and certain applications in geometric function theory

Integral Transformation, Operational Calculus and Their Applications

The importance and usefulness of subjects and topics involving integral transformations and operational calculus are becoming widely recognized, not only in the mathematical sciences but also in the physical, biological, engineering and statistical sciences. This book contains invited reviews and expository and original research articles dealing with and presenting state-of-the-art accounts of the recent advances in these important and potentially useful subjects

Geometrical Theory of Analytic Functions

The book contains papers published in the Mathematics Special Issue, entitled "Geometrical Theory of Analytic Functions". Fifteen papers devoted to the study concerning complex-valued functions of one variable present new outcomes related to special classes of univalent functions, differential equations in view of geometric function theory, quantum calculus and its applications in geometric function theory, operators and special functions associated with differential subordination and superordination theories and starlikeness, and convexity criteria

An Investigation of the Third Hankel Determinant Problem for Certain Subfamilies of Univalent Functions Involving the Exponential Function

In the current article, we consider certain subfamilies S e &#8727; and C e of univalent functions associated with exponential functions which are symmetric along real axis in the region of open unit disk. For these classes our aim is to find the bounds of Hankel determinant of order three. Further, the estimate of third Hankel determinant for the family S e &#8727; in this work improve the bounds which was investigated recently. Moreover, the same bounds have been investigated for 2-fold symmetric and 3-fold symmetric functions