arXiv subjects

S. Sivaprasad Kumar

Publications and source records attributed to S. Sivaprasad Kumar.

60 records · Page 4Linked to original sources

arXiv2020

A Cardioid Domain and Starlike Functions

We introduce and study a class of starlike functions defined by \begin{equation*} \mathscr{S}^*_\wp:=\left\{f\in\mathcal{A}: \frac{zf'(z)}{f(z)}\prec 1+ze^z=:\wp(z)\right\}, \end{equation*} where $\wp$ maps the unit disk onto a cardioid domain. We find the radius of convexity of $\wp(z)$ and establish the inclusion relations between the class $ \mathscr{S}^*_\wp$ and some well-known classes. Further we derive sharp radius constants and coefficient related results for the class $ \mathscr{S}^*_\wp$.

math.CV↗

arXiv2019

The sharp bounds of the second and third Hankel determinants for the class SL^*

The aim of the present paper is to obtain the sharp bounds of the Hankel determinants H_2(3) and H_3(1) for the well known class SL^* of starlike functions associated with the right lemniscate of Bernoulli. Further for n=3, we find the sharp bound of the Zalcman functional for the class SL^*. In addition, a couple of interesting results of SL^* is appended at the end.

math.CV↗

arXiv2013

Sufficient Conditions for Starlike Functions Associated with the Lemniscate of Bernoulli

Let -1\leq B<A\leq 1. Condition on β, is determined so that 1+βzp'(z)/p^k(z)\prec(1+Az)/(1+Bz)\;(-1<k\leq3) implies p(z)\prec \sqrt{1+z}. Similarly, condition on βis determined so that 1+βzp'(z)/p^n(z) or p(z)+βzp'(z)/p^n(z)\prec\sqrt{1+z}\;(n=0, 1, 2) implies p(z)\prec(1+Az)/(1+Bz) or \sqrt{1+z}. In addition to that condition on βis derived so that p(z)\prec(1+Az)/(1+Bz) when p(z)+βzp'(z)/p(z)\prec\sqrt{1+z}. Few more problems of the similar flavor are also considered.

math.CV↗

arXiv2013

Estimates for the Initial Coefficients of Bi-univalent Functions

A bi-univalent function is a univalent function defined on the unit disk with its inverse also univalent on the unit disk. Estimates for the initial coefficients are obtained for bi-univalent functions belonging to certain classes defined by subordination and relevant connections with earlier results are pointed out.

math.CV↗

arXiv2012

On the Fekete-Szegö inequality for Certain class of analytic functions

In the present investigation, we derive Fekete-Szegö inequality for the class $\mathcal{S}^α_{\mathscr{L}_{g}}(ϕ)$, introduced here. In addition to that, certain applications of our results are also discussed.

math.CV↗

arXiv2011

Subordination and superordination for multivalent functions defined by linear operators

In this paper, certain linear operators defined on $p$-valent analytic functions have been unified and for them some subordination and superordination results as well as the corresponding sandwich type results are obtained. A related integral transform is discussed and sufficient conditions for functions in different classes have been obtained.

math.CV↗