Sharp Estimate of Fifth Coefficient for Ma Minda Starlike and Convex Functions

Surya Giri; S. Sivaprasad Kumar

Sharp Estimate of Fifth Coefficient for Ma Minda Starlike and Convex Functions

Complex Variables 2023-10-11 v4

Authors: Surya Giri , S. Sivaprasad Kumar

Abstract

\noindent In the present investigation, we find the sharp bound of fifth coefficient of analytic normalized function $f$ satisfying $z f'(z)/f(z) \prec \varphi(z)$ when coefficients of $\varphi$ satisfy certain conditions. For an appropriate choice of $\varphi$ , the already known estimates for various other subclasses of starlike functions follow directly from the obtained result.

Keywords

fifth coefficient ma minda starlike functions convex functions sharp bound subordination analytic normalized function

Cite

@article{arxiv.2201.05803,
  title  = {Sharp Estimate of Fifth Coefficient for Ma Minda Starlike and Convex Functions},
  author = {Surya Giri and S. Sivaprasad Kumar},
  journal= {arXiv preprint arXiv:2201.05803},
  year   = {2023}
}

Comments

paper revised and results improved

Related papers

View all related →