Sushil Kumar

Bharati Vidyapeeth College of Engineering, New Delhi · Applied Sciences

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...

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 Zal...

Differential subordination in the complex plane is the generalization of a differential inequality on the real line. In this paper, we consider two subclasses of univalent functions associated with the trigonometric function $\cos z$. Using some properties of the hypergeometric functions, we determine the sharp estimate on the parameter $\beta$ suc...

In this paper, we consider the class of starlike functions with respect to symmetric points which are also known as Sakaguchi starlike functions. We de- termine best possible bounds on Zalcman conjecture |a_n^2 – a_(2n-1) | and generalized Zalcman conjecture |aman − am+n−1| for n = 2 and n = 4, m = 2, respectively for such functions. Further, we co...

Let \(\mathcal {P}\) 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 \(\beta \) such that the analytic function \(p\in \mathcal {P}\) is subordinate to certain functions having positive real part whenever \(p(z)...

The goal of this paper is to establish the sharp estimates on coefficient functionals like Hermitian–Toeplitz determinant of second-order involving logarithmic coefficients, initial logarithmic inverse coefficients as well as sharp bounds on initial order Schwarzian derivatives of the Ozaki close-to-convex functions.

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 $f \in \mathcal{ST}_{lh}(s)$. Fur...

"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, Carathéodo...

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-Toep...

The association of subordination and special functions is used to find sharp estimates on the parameter $\beta$ such that the analytic function $p(z)$ is subordinate to certain functions having positive real part whenever $p(z)+\beta z p'(z)$ is subordinate to the Janowski function. Further, when the traditional approach of solving higher order dif...

Let $\mathcal{P}$ denote the Carath\'{e}odory 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 t...

A normalized analytic function f is parabolic starlike if w(z) := zf′ (z)/f(z) maps the unit disk into the parabolic region {w : Re w > |w − 1|}. Sharp estimates on the third Hermitian-Toeplitz determinant are obtained for parabolic starlike functions. In addition, upper bounds on the third Hankel determinants are also determined.

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 esti...

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 logarith...

Several properties of the class S∗r(α) of starlike functions of reciprocal order α (0 ≤ α < 1) defined on the open unit disk have been studied in this paper. The paper begins with a sufficient condition for analytic functions to be in the class S∗r(α). Further, the sharp bounds on third order HermitianToeplitz determinant, initial inverse coefficie...

In this paper, sharp lower and upper bounds on the third order Hermitian-Toeplitz determinant for the classes of Sakaguchi functions and some of its subclasses related to right-half of lemniscate of Bernoulli, reverse lemniscate of Bernoulli and exponential functions are investigated.

This paper aims to pursue some classes of normalized analytic functions $f$ with fixed second coefficient defined on open unit disk, such that ${(1+z)^2f(z)}/{z}$ 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 s...

In this manuscript, we deal with three classes of quotient functions having fixed second coefficient described on open unit disk. The radius of strongly starlikeness, lemniscate starlikeness, lune starlikeness, parabolic starlikeness, sine starlikeness, exponential starlikeness and several other radius estimates for such classes are examined. Relev...

Let ϕ be a normalized convex function defined on open unit disk D. For a unified class of normalized analytic functions which satisfy the second order differential subordination f′(z) + αzf″(z) ≺ ϕ(z) for all z∈D, we investigate the distortion theorem and growth theorem. Further, the bounds on initial logarithmic coefficients, inverse coefficient a...

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 \begin{document}$ \tanh z $\end{document}. We also determine sharp bounds on second and third order Hermitian-Toeplitz determinants for such functions. Further, we compute estimates...

In this paper, we study geometric properties of a class of multivalent functions with negative coefficients that are connected with the generalized Mittag-Leffler functions. 2010 Mathematics Subject Classification: 30C45, 30C50.

Numerical techniques are used to determine the radius of convexity of the starlike functions related to cardioid shaped bounded domain. In addition, radius constants of certain starlikeness associated with right half plane of various starlike functions are computed.

"Theory of differential subordination provides techniques to reduce differential subordination problems into verifying some simple algebraic condition called admissibility condition.We exploit the first order differential subordination theory to get several sufficient conditions for function satisfying several differential subordinations to be a Ja...

Ma–Minda class (of starlike functions) consists of normalized analytic functions f defined on the unit disk for which the image of the function zf′(z)/f(z) is contained in some starlike region lying in the right-half plane. In this paper, we obtain the best possible bounds on some initial coefficients for the inverse functions of Ma–Minda starlike...

The sharp upper and lower bounds on the Hermitian-Toeplitz determinant of third order are computed for the classes of strongly starlike functions, lemniscate starlike functions and lune starlike functions. Moreover, a non-sharp upper bound on the fourth Hankel determinant for the lemniscate starlike functions is also obtained. Relevant connections...

Some sufficient conditions on certain constants which are involved in some first and second-order differential subordinations associated with certain functions with positive real part like modified Sigmoid function, exponential function and Janowski function are obtained so that the analytic function [Formula: see text] normalized by the condition...

The sharp lower and upper estimates on the second- and third-order Hermitian–Toeplitz determinants for the classes of starlike functions associated with the modified sigmoid function and a related function, whose Taylor coefficients are the Bell numbers, are investigated. Further, the third and fourth Hankel determinants for these classes are also...

In this paper, we introduce new classes of post-quantum or (p, q)-starlike and convex functions with respect to symmetric points associated with a cardiod-shaped domain. We obtain (p, q)-Fekete-Szegö inequalities for functions in these classes. We also obtain estimates of initial (p, q)-logarithmic coefficients. In addition, we get q-Bieberbach-de-...

In this article, we wish to establish some first order differential subordination relations for certain Carath\'{e}odory functions with nice geometrical properties. Moreover, several implications are determined so that the normalized analytic function belongs to various subclasses of starlike functions.

The Bohr radius for a class \({\mathcal {G}}\) consisting of analytic functions \(f(z)=\sum _{n=0}^{\infty }a_nz^n\) in unit disc \({\mathbb {D}}=\{z\in {\mathbb {C}}:|z|<1\}\) is the largest \(r^*\) such that every function f in the class \({\mathcal {G}}\) satisfies the inequality $$\begin{aligned} d\left( \sum _{n=0}^{\infty }|a_nz^n|, |f(0)|\ri...

Some sufficient conditions on certain constants which are involved in some first, second and third order differential subordinations associated with certain functions with positive real part like modified Sigmoid function, exponential function and Janowski function are obtained so that the analytic function p normalized by the condition p(0) = 1, i...

The Bohr radius for a class $\mathcal{G}$ consisting of analytic functions $f(z)=\sum_{n=0}^{\infty}a_nz^n$ in unit disc $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$ is the largest $r^*$ such that every function $f$ in the class $\mathcal{G}$ satisfies the inequality \begin{equation*} d\left(\sum_{n=0}^{\infty}|a_nz^n|, |f(0)|\right) = \sum_{n=1}^{\infty}...

Let $\phi$ be a normalized convex function defined on open unit disk $\mathbb{D}$. For a unified class of normalized analytic functions which satisfy the second order differential subordination $f'(z)+ \alpha z f''(z) \prec \phi(z)$ for all $z\in \mathbb{D}$, we investigate the distortion theorem and growth theorem. Further, the bounds on initial l...

There exists a rich literature on the Hankel determinants in the field of geometric function theory. Particularly, it is not easy to find out the sharp bound on the third Hankel determinant as compared to calculate the sharp bound on the second Hankel determinant. The present paper is an attempt to improve certain existing bound on the third Hankel...

By using admissibility condition technique, certain sufficient conditions are determined so that an analytic function p defined on the open unit disk and normalized by \(p(0) = 1\) satisfy the subordination \(p(z) \prec (1+Az)/(1+Bz)\) whenever, for certain choice of \(\psi \), the function \(\psi (p(z), zp'(z))\) is subordinate to a starlike funct...

Ma-Minda class (of starlike functions) consists of all normalized analytic functions f on the unit disk for which the image of zf′(z)/f(z) is contained in the some starlike region in the right-half plane. We obtain the best possible bounds on the second and third coefficient for the inverse functions of functions in the Ma-Minda class. The bounds o...

Theory of differential subordination provides techniques to reduce differential subordination problems into verifying some simple algebraic condition called admissibility condition. We exploit the first order differential subordination theory to get several sufficient conditions for function satisfying several differential subordinations to be a Ja...

The present paper aims to establish the first order differential subordination relations between functions with a positive real part and starlike functions related to the Bell numbers. In addition, several sharp radii estimates for functions in the class of starlike functions associated with the Bell numbers are determined.

Abstract. The concept of convolution is applied to investigate some subordination results for the normalized analytic functions whose first derivative belongs to the class of the tilted Caratheodory functions. The sharp radius of starlikeness of order $\alpha$ of the product of two normalized analytic functions satisfying certain specified conditio...

Some sufficient conditions are determined for certain first order differential subordinations to imply the corresponding analytic solution is subordinate to a rational, exponential, or sine function. By applying these results, we also obtain sufficient conditions for normalized analytic functions to be in certain well known subclasses of starlike f...

The well-known theory of differential subordination developed by Miller and Mocanu is applied to obtain several inclusions between Carathéodory functions and starlike functions. These inclusions provide sufficient conditions for normalized analytic functions to belong to certain class of Ma-Minda starlike functions.

We obtain several inclusions between the class of functions with positive real part and the class of starlike univalent functions associated with the Booth lemniscate. These results are proved by applying the well-known theory of differential subordination developed by Miller and Mocanu and these inclusions give sufficient conditions for normalized...

The sharp bounds for the third and fourth coefficients of Ma-Minda starlike functions having fixed second coefficient are determined. These results are proved by using certain constraint coefficient problem for functions with positive real part whose coefficients are real and the first coefficient is kept fixed. Analogous results are obtained for a...

In this paper, sharp radii constants are obtained for the analytic functions satisfying some coefficient inequalities. For such functions, growth and distortion estimates are determined. In addition, it is proved that functions in these classes are closed under Hadamard product with convex functions.

Sharp estimates on $\beta$ are determined so that an analytic function $p$ defined on the open unit disk in the complex plane normalized by $p(0)=1$ is subordinate to some well known starlike functions with positive real part whenever $1+\beta z p'(z), \,\,1+\beta z p'(z)/p(z), \,\,\mbox{or}\,\,1+\beta z p'(z)/p^{2}(z)$ is subordinate to $\sqrt{1+z...

For -1 ≤ B < A ≤ 1, let S∗[A,B] and K[A,B] be the classes of analytic functions f defined in the open unit disk normalized by the conditions f(0) = f'(O) \- 1 = 0 satisfying the subordination relations zf'(z)/f(z) < (1 + Az)/(1 + Bz) and 1 + zf"(z)/f'(z)<(1 + Az)/(1 + Bz) respectively. The necessary and sufficient coefficient conditions are obtaine...