Coefficient inequalities for certain starlike and convex functions

Authors : Sushil Kumar KUMAR, Asena ÇETİNKAYA

Pages : 156-171

Doi:10.15672/hujms.778148

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Publication Date : 2022-02-14

Article Type : Research Paper

Abstract :In this paper, we consider two Ma--Minda-type subclasses of starlike and convex functions associated with the normalized analytic function $\varphi_{Ne}insert ignore into journalissuearticles values(z);=1+z-z^3/3$ 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