- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
 Sufficient conditions for univalence and study of a class of meromorphic univalent functions Bull. Korean Math. Soc. 2018 Vol. 55, No. 3, 999-1006 https://doi.org/10.4134/BKMS.b170465Published online May 31, 2018 Bappaditya Bhowmik, Firdoshi Parveen Indian Institute of Technology Kharagpur, Indian Institute of Technology Kharagpur Abstract : In this article we consider the class $\mathcal{A}(p)$ which consists of functions that are meromorphic in the unit disc $\ID$ having a simple pole at $z=p\in (0,1)$ with the normalization $f(0)=0=f'(0)-1$. First we prove some sufficient conditions for univalence of such functions in $\ID$. One of these conditions enable us to consider the class $\mathcal{V}_{p}(\lambda)$ that consists of functions satisfying certain differential inequality which forces univalence of such functions. Next we establish that $\mathcal{U}_{p}(\lambda)\subsetneq \mathcal{V}_{p}(\lambda)$, where $\mathcal{U}_{p}(\lambda)$ was introduced and studied in \cite{BF-1}. Finally, we discuss some coefficient problems for $\mathcal{V}_{p}(\lambda)$ and end the article with a coefficient conjecture. Keywords : meromorphic functions, univalent functions, subordination, Taylor coefficients MSC numbers : 30C45, 30C55 Downloads: Full-text PDF