- 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
 Logharmonic mappings with typically real analytic components Bull. Korean Math. Soc. 2018 Vol. 55, No. 6, 1783-1789 https://doi.org/10.4134/BKMS.b171072Published online June 29, 2018Printed November 30, 2018 Zayid AbdulHadi, Najla M. Alarifi, Rosihan M. Ali American University of Sharjah, Imam Abdulrahman Bin Faisal University, University Sains Malaysia Abstract : This paper treats the class of normalized logharmonic mappings $f(z)=zh(z)\overline{g(z)}$ in the unit disk satisfying $\varphi(z)=zh(z)g(z)$ is analytically typically real. Every such mapping $f$ admits an integral representation in terms of its second dilatation function and a function of positive real part with real coefficients. The radius of starlikeness and an upper estimate for arclength are obtained. Additionally, it is shown that $f$ maps the unit disk into a domain symmetric with respect to the real axis when its second dilatation has real coefficients. Keywords : logharmonic mappings, typically real functions, radius of starlikeness, arclength MSC numbers : Primary 30C35, 30C45 Downloads: Full-text PDF