Searcharxiv⌕ Search

arXiv subjects

Naveen Kumar Jain

Publications and source records attributed to Naveen Kumar Jain.

13 recordsLinked to original sources
arXiv2026

Sharp Bohr-Type inequalities for certain classes of close-to-convex functions

In this article, we determine the Rogosinski radii for certain subclasses of close-to-convex functions defined on open unit disc $\mathbb{D}= \{z \in \mathbb{C}: |z| < 1\}$. Furthermore, we establish improved versions of the classical Bohr inequality and the Bohr-Rogosinski inequality pertaining to these subclasses. We demonstrate that all results derived in the study are sharp.

math.CV↗
arXiv2023

Starlikeness Using Special Functions and Subordination

The association of subordination and special functions is used to find sharp estimates on the parameter $β$ such that the analytic function $p(z)$ is subordinate to certain functions having positive real part whenever $p(z)+βz p'(z)$ is subordinate to the Janowski function. Further, when the traditional approach of solving higher order differential subordination implications failed, 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 demonstrated the starlikeness of various well-known analytic functions as well.

math.CV↗
arXiv2023

Constrained Radius Estimates Of Certain Analytic Functions

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.

math.CV↗
arXiv2022

Radii Constants for Functions with Fixed Second Coefficient

We introduce three classes of analytic functions with fixed second coefficient which are defined using the class $\mathcal{P}$ of analytic functions with positive real part. The objective is to determine radii such that the three classes are contained in various subclasses of starlike functions. The radii estimated in the present investigation are better than the radii obtained earlier. Furthermore, connections with previous known results are shown.

math.CV↗
arXiv2022

Generalized radius problems for quotient functions having fixed second coefficient

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. Relevant relations of obtained radius estimates with the existing estimates are also discussed.

math.CV↗
arXiv2022

Certain subclasses of Analytic Functions with Fixed Second Coefficient

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 starlikeness estimates are calculated for such functions. As well relevant connections of computed radii estimates with the existing one are also shown.

math.CV↗
arXiv2021

Differential Subordination implications for Certain Carathéodory functions

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.

math.CV↗
arXiv2021

Analytic functions with conic domains associated with certain generalized q-integral operator

In this paper, we define a new subclass of $k$-uniformly starlike functions of order $γ,\ (0\leqγ<1)$ by using certain generalized $q$-integral operator. We explore geometric interpretation of the functions in this class by connecting it with conic domains. We also investigate $q$-sufficient coefficient condition, $q$-Fekete-Szegö inequalities, $q$-Bieberbach-De Branges type coefficient estimates and radius problem for functions in this class. We conclude this paper by introducing an analogous subclass of $k$-uniformly convex functions of order $γ$ by using the generalized $q$-integral operator. We omit the results for this new class because they can be directly translated from the corresponding results of our main class.

math.CV↗
arXiv2020

Differential Subordinations For Functions With Positive Real Part Using Admissibility Conditions

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, is subordinate to Janowski function. The admissibility conditions for Janowski function are used as a tool in the proof of the results. As application, several sufficient conditions are also computed for Janowski starlikeness.

math.CV↗
arXiv2020

Sharp Bohr Radius Constants For Certain Analytic 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{equation*} d\left(\sum_{n=0}^{\infty}|a_nz^n|, |f(0)|\right) = \sum_{n=1}^{\infty}|a_nz^n|\leq d(f(0), \partial f(\mathbb{D})) \end{equation*} for all $|z|=r \leq r^*$, where $d$ is the Euclidean distance. In this paper, our aim is to determine the Bohr radius for the classes of analytic functions $f$ satisfying differential subordination relations $zf'(z)/f(z) \prec h(z)$ and $f(z)+βz f'(z)+γz^2 f''(z)\prec h(z)$, where $h$ is the Janowski function. Analogous results are obtained for the classes of $α$-convex functions and typically real functions, respectively. All obtained results are sharp.

math.CV↗
arXiv2020

Certain Estimates of Normalized Analytic Functions

Let $ϕ$ 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 $f'(z)+ αz f''(z) \prec ϕ(z)$ for all $z\in \mathbb{D}$, we investigate the distortion theorem and growth theorem. Further, the bounds on initial logarithmic coefficients, inverse coefficient and the second Hankel determinant involving the inverse coefficients are examined.

math.CV↗