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Bappaditya Bhowmik

Publications and source records attributed to Bappaditya Bhowmik.

20 records · Page 2Linked to original sources

arXiv2015

Quasiconformal extension of meromorphic functions with nonzero pole

In this note, we consider meromorphic univalent functions $f(z)$ in the unit disc with a simple pole at $z=p\in(0,1)$ which have a $k$-quasiconformal extension to the extended complex plane $\hat{\mathbb C},$ where $0\leq k < 1$. We denote the class of such functions by $Σ_k(p)$. We first prove an area theorem for functions in this class. Next, we derive a sufficient condition for meromorphic functions in the unit disc with a simple pole at $z=p\in(0,1)$ to belong to the class $Σ_k(p)$. Finally, we give a convolution property for functions in the class $Σ_k(p)$.

math.CV↗

arXiv2010

Coefficient Inequalities for Concave and Meromorphically Starlike Univalent Functions

Let $\ID$ denote the open unit disk and $f:\,\ID\TO\BAR\IC$ be meromorphic and univalent in $\ID$ with the simple pole at $p\in (0,1)$ and satisfying the standard normalization $f(0)=f'(0)-1=0$. Also, let $f$ have the expansion $$f(z)=\sum_{n=-1}^{\infty}a_n(z-p)^n,\quad |z-p|<1-p, $$ such that $f$ maps $\ID$ onto a domain whose complement with respect to $\BAR{\IC}$ is a convex set (starlike set with respect to a point $w_0\in \IC, w_0\neq 0$ resp.). We call these functions as concave (meromorphically starlike resp.) univalent functions and denote this class by $Co(p)$ $(Σ^s(p, w_0)$ resp.). We prove some coefficient estimates for functions in the classes where the sharpness of these estimates is also achieved.

math.CV↗