- Hacettepe Journal of Mathematics and Statistics
- Vol: 51 Issue: 1
- Coefficient inequalities for certain starlike and convex functions
Coefficient inequalities for certain starlike and convex functions
Authors : Sushil Kumar Kumar, Asena Çetinkaya
Pages : 156-171
Doi:10.15672/hujms.778148
View : 14 | Download : 4
Publication Date : 2022-02-14
Article Type : Research
Abstract :In this paper, we consider two Ma--Minda-type subclasses of starlike and convex functions associated with the normalized analytic function $\varphi_{Ne}(z)=1+z-z^3/3$ that maps an open unit disk onto the Nephroid shaped bounded domain in the right--half of the complex plane. We investigate convolution and quasi-Hadamard product properties for the functions belonging to such classes. In addition, we compute best possible estimates on third order Hermitian--Toeplitz determinant and non-sharp estimates on certain third order Hankel determinants for the starlike functions associated with the interior region of Nephroid.Keywords : Starlike functions, convex functions, Neproid, convolution properties, quasi-Hadamard product properties, Hermitian--Toeplitz and Hankel determinants