arXiv subjects
Publications and source records attributed to Nisha Bohra.
A harmonic mapping $f=h+\overline{g}$ in $\mathbb{D}$ is $φ$-normal if $f^{\#}(z)=\mathcal{O}(|φ(z)|), \text{ as } |z|\to 1^-,$ where $f^{\#}(z)={(|h'(z)|+|g'(z)|)}/{(1+|f(z)|^2)}.$ In this paper, we establish several sufficient conditions for harmonic mappings to be $φ$-normal. We also extend the five-point theorem of Lappan for $φ$-normal harmonic mappings.
Estimates for initial coefficients of Taylor-Maclaurin series of bi-univalent functions belonging to certain classes defined by subordination are obtained. Our estimates improve upon the earlier known estimates for second and third coefficient. The bound for the fourth coefficient is new. In addition, bound for the fifth coefficient is obtained for bi-starlike and strongly bi-starlike functions of order $ρ$ and $β$ respectively.