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Sarita Agrawal

Publications and source records attributed to Sarita Agrawal.

7 recordsLinked to original sources
arXiv2020

Nehari's univalence criteria, pre-Schwarzian derivative and applications

In this paper we study sharp estimates of pre-Schwarzian derivatives of functions belonging to the Nehari-type classes by using techniques from differential equations. In the sequel, we also see that a solution of a complex differential equation has a special form in terms of ratio of hypergeometric functions resulting to an integral representation. Finally, we attempt to study those univalent functions in the unit disk for which the image domain is an unbounded John domain.

math.CV↗
arXiv2018

On a generalization of starlike functions

In this paper, we mainly study the order of $q$-starlikeness of the well-known basic hypergeometric function. In addition, we obtain the Bieberbach-type problem for a generalized class of starlike functions. We also discuss the Fekete-szegö and the Hankel determinant problems for the same class of functions.

math.CV↗
arXiv2017

Coefficient estimates for some classes of functions associated with \(q\)-function theory

In this paper, for every $q\in(0,1)$, we obtain the Herglotz representation theorem and discuss the Bieberbach type problem for the class of $q$-convex functions of order $α, 0\leα<1$. In addition, we discuss the Fekete-szegö problem and the Hankel determinant problem for the class of $q$-starlike functions, leading to couple of conjectures for the class of $q$-starlike functions of order $α, 0\leα<1$.

math.CV↗
arXiv2016

On coefficient functionals associated with the Zalcman conjecture

We consider certain subfamilies, of the family of univalent functions in the open unit disk, defined by means of sufficient coefficient conditions for univalency. This article is devoted to studying the problem of the well-known conjecture of Zalcman consisting of a generalized coefficient functional, the so-called generalized Zalcman conjecture problem, for functions belonging to those subfamilies. We estimate the bounds associated with the generalized coefficient functional and show that the estimates are sharp.

math.CV↗
arXiv2016

Radius of convexity of partial sums of odd functions in the close-to-convex family

We consider the class of all analytic and locally univalent functions $f$ of the form $f(z)=z+\sum_{n=2}^\infty a_{2n-1} z^{2n-1}$, $|z|<1$, satisfying the condition $$ {\rm Re}\,\left(1+\frac{zf^{\prime\prime}(z)}{f^\prime (z)}\right)>-\frac{1}{2}. $$ We show that every section $s_{2n-1}(z)=z+\sum_{k=2}^na_{2k-1}z^{2k-1}$, of $f$, is convex in the disk $|z|<\sqrt{2}/3$. We also prove that the radius $\sqrt{2}/3$ is best possible, i.e. the number $\sqrt{2}/3$ cannot be replaced by a larger one.

math.CV↗
arXiv2015

A generalization of starlike functions of order alpha

For every $q\in(0,1)$ and $0\le α<1$ we define a class of analytic functions, the so-called $q$-starlike functions of order $α$, on the open unit disk. We study this class of functions and explore some inclusion properties with the well-known class of starlike functions of order $α$. The paper is also devoted to the discussion on the Herglotz representation formula for analytic functions $zf'(z)/f(z)$ when $f(z)$ is $q$-starlike of order $α$. As an application we also discuss the Bieberbach conjecture problem for the $q$-starlike functions of order $α$. Further application includes the study of the order of $q$-starlikeness of the well-known basic hypergeometric functions introduced by Heine.

math.CV↗
arXiv2014

Geometric properties of basic hypergeometric functions

In this paper we consider basic hypergeometric functions introduced by Heine. We study mapping properties of certain ratios of basic hypergeometric functions having shifted parameters and show that they map the domains of analyticity onto domains convex in the direction of the imaginary axis. In order to investigate these mapping properties, few useful identities are obtained in terms of basic hypergeometric functions. In addition, we find conditions under which the basic hypergeometric functions are in $q$-close-to-convex family.

math.CV↗