In this paper, we consider two classes KS and SS & lowast; of convex and starlike functions with respect to symmetric points respectively. We determine bounds on Hankel determinants and Hermitian-Toeplitz determinants involving initial coefficients, initial inverse and initial logarithmic coefficients for such functions with missing second coefficient. Analogous results are also established for two subclasses of SS & lowast; which are associated with the lemniscate of Bernoulli and the exponential function, respectively.

In this paper, we define new subclasses $\mathcal{ST}_{lh}(s)$ and $\mathcal{CST}_{lh}(s)$ of sin starlike log-harmonic mappings and sin close to starlike log-harmonic mappings, respectively, defined in the open unit disc $\de$. We investigate representation theorem and integral representation theorem for functions $f \in \mathcal{ST}_{lh}(s)$. Further, we determine radii of starlikeness for such functions.

This article aims at exploring various geometric properties of entire functions, followed by some results related to differential equations and special functions. It focuses on the monotonicity of the normalized Miller-Ross function and further identifying adequate conditions for it to belong to certain subclasses of starlike functions. Additionally, the article provides various relations to ensure that the solution of a certain second-order differential equation is subordinate to the Janowski function. These findings are illustrated through a variety of examples involving certain entire functions.

The growth and distortion theorems provide bounds on how much a univalent function can stretch or distort distances and shapes in the complex plane. It is closely associated with the theory of univalent functions. The radius estimates in univalent function theory offer valuable insights into the behavior of analytic and univalent functions, helping to determine the domains within which these functions maintain various properties such as starlikeness, convexity, close-to-convexity, etc. The main aim of this manuscript is to investigate the growth and distortion theorem, as well as various types of radius estimates, for a certain class of quotient functions with a fixed second coefficient defined on the open unit disk.

In this paper, we introduce a subclass of close-to-convex functions associated with a cubic polynomial 1 + z - (z(3)/3) which is a Caratheodary function and related to the nephroid shaped bounded domain. We discuss the growth and distortion theorems and certain coefficient inequalities using the concept of subordination for such functions. We also determine bounds on initial coefficients, inverse coefficients, logarithmic coefficients and logarithmic inverse coefficients. Moreover, we compute bounds of the second order Hankel determinants and Schwarzian derivatives.

In this paper, we consider a subclass of normalized analytic functions associated with the hyperbolic secant function. We compute the sharp bounds on third- and fourth-order Hermitian–Toeplitz determinants for functions in this class. Moreover, we determine the bounds on second- and third-order Hankel determinants, as well as on the generalized Zalcman conjecture. We examine a Briot–Bouquet-type differential subordination involving the Bernardi integral operator. Finally, we obtain a univalent solution to the Briot–Bouquet differential equation, and discuss the majorization property for such function classes.

In this paper, we consider the class K-S (psi(0)) of close-to-convex functions associated to a rational function psi(0)(z) = (k(2) + z(2))/(k(2) - kz), where k = root 2 + 1 and the rational function psi(0) is related to cardioid shaped bounded domain. We compute the radius of convexity, growth, distortion and certain coefficient inequalities of such functions. We determine bounds on second and third order Toeplitz determinants. Moreover, we also compute bounds on second order Hankel determinants and second and third order Vandermonde determinants. (c) 2024 Mathematical Institute Slovak Academy of Sciences

The goal of this manuscript to establish the best possible estimate on coefficient functionals like Hermitian-Toeplitz determinant of secoend order involving logarithmic coefficients, initial logarithmic inverse coefficients and initial order Schwarzian derivatives of the Ozaki close-to-convex functions.

In this paper, we study the second order Hermitian-Toeplitz determinant for the functions belonging to certain subclasses of univalent functions defined in the open unit disk in the Argand plane. In the demonstration of the proofs, we apply some coefficients inequalities for functions with positive real part due to Libera and Zlotkiewicz [12].

Let 𝒫 be the class of analytic functions having positive real part in the complex plane. The association of subordination and special functions is used to find sharp estimates on the parameter β such that the analytic function p∈𝒫 is subordinate to certain functions having positive real part whenever p(z)+β z p'(z) is subordinate to the Janowski function. Further, the concept of admissibility is employed to establish certain second and third order differential subordination relations between the analytic function p and the functions associated with right half plane. As a sequel, we demonstrate the starlikeness of various well-known analytic functions as well.

In this paper, we consider the class of starlike functions with respect to symmetric points which are also known as Sakaguchi starlike functions. We determine best possible bounds on Zalcman conjecture |a(n)( 2 ) -a(2n-1)| and generalized Zalcman conjecture |a(m)a(n) - a(m+n-1)| for n = 2 and n = 4, m = 2, respectively for such functions. Further, we compute estimate on third order and fourth order Hankel determinants. As well, we also obtain estimates on third and fourth symmetric Toeplitz determinants.

In this paper, we determine sharp bounds on some Hankel determinants involving initial coefficients, inverse coefficients, and logarithmic inverse coefficients for two associated subclasses of Sakaguchi functions related to the lemniscate of Bernoulli and exponential function. Further, we compute sharp bounds on the second-order Hermitian–Toeplitz determinants involving logarithmic coefficients and logarithmic inverse coefficients for such subclasses. We also discuss the invariance property for the obtained estimates with respect to various coefficients.

In this paper, we investigate some geometric properties of starlikeness connected with the hyperbolic cosine functions defined in the open unit disk. In particular, for the class of such starlike hyperbolic cosine functions, we determine the lower bounds of partial sums, BriotBouquet differential subordination associated with Bernardi integral operator, and bounds on some third Hankel determinants containing initial coefficients.

Let $\mathcal{P}$ denote the Carathéodory class accommodating all the analytic functions $p$ having positive real part and satisfying $p(0)=1$. In this paper, the second coefficient of the normalized analytic function $f$ defined on the open unit disc is constrained to define new classes of analytic functions. The classes are characterised by the functions $f/g$ having positive real part or satisfying the inequality $|(f(z)/g(z))-1|<1$ such that $f(z)(1-z^2)/z$ and $g(z)(1-z^2)/z$ are Carathéodory functions for some analytic function $g$. This paper aims at determining radius of starlikeness for the introduced classes.

We determine the upper bounds on fourth order Hankel de-terminants H4(2) (f) and H(3) 4 (f) for the class S*L of lemniscate starlike functions defined on the open unit disk which was introduced by Sok ' o l and Stankiewicz in [17].

"In this article, we wish to establish some first order differential subordination relations for certain Carathéodory functions with nice geometrical properties. Moreover, several implications are determined so that the normalized analytic function belongs to various subclasses of starlike functions. Keywords: Differential subordination, Carathéodory function, starlike functions, sufficient conditions."

This paper studies normalized analytic functions f with fixed second coefficient defined on open unit disk for which (1+z)^2f(z)/z and (1+z)f(z)/z are functions having positive real part. The radius of strongly starlikeness, the radius of lemniscate starlikeness, the radius of parabolic starlikeness and other starlikeness radii estimates are calculated for these functions. As well relevant connections of computed radii estimates with the existing one are also shown.

In this paper, we explore a subfamily of starlike functions with respect to symmetric points allied with the hyperbolic cosine function. We study Hermitian–Toeplitz determinants of third and fourth orders for the functions belonging to this subfamily. Further, we calculate estimates on the initial successive inverse coefficients as well as logarithmic coefficients and related functionals for such functions. In addition, we also determine bounds on Hankel determinants of third order and symmetric Toeplitz determinants of second and third orders.

We determine sharp bounds on some Hankel determinants involving initial coefficients, inverse coefficients, and logarithmic inverse coefficients for two subclasses of Sakaguchi functions which are associated with the right half of the lemniscate of Bernoulli and the exponential function. Further, we compute sharp bounds on the second Hermitian-Toeplitz determinants involving logarithmic coefficients and logarithmic inverse coefficients. We also discuss invariant property for the obtained estimates with respect to various coefficients.

We determine the necessary and sufficient convolution conditions for the starlike functions on the open unit disk and related to some geometric aspects of the function tanh z. We also determine sharp bounds on second and third order Hermitian-Toeplitz determinants for such functions. Further, we compute estimates on some initial coefficients and the Hankel determinants of third and fourth order. In addition, using the concept of Briot-Bouquet type differential subordination, we establish a subordination inclusion involving Bernardi integral operator.