Bounds of Coefficient Functional of Certain Subclasses of Analytic Functions Associated with Cardioid Domain

Abstract

In the present paper with the aid of subordination, the authors introduce a new subclass of univalent functions namely; starlike functions with respect to symmetric points linked with cardioid domain defined by $S_{s,e}^{**} := \left\{ f \in \mathcal{S}: \frac{2zf^{\prime}(z)}{f(z)-f(-z)} \prec 1+ze^z=:p(z)\right\}$, where the function $p(z)$ maps unit disk $\mathbb{D}:=\{z \in \mathbb{C}: |z|<1\}$ onto a cardioid domain in the right half plane. We investigate the sharp upper bounds of some of the initial coefficients, Fekete-Szeg\"{o} functional and Hankel determinant involving initial coefficients of function $f$ for the class $S_{s, e}^{**}$. Further, we determine some of the sharp bounds of logarithmic inverse coefficients, Hankel, Toeplitz, Hermitian-Toeplitz determinant, Zalcman functional, Kruskal inequality as well as the lower and upper bounds for modulo difference of second and the first logarithmic inverse coefficient for such family. Also we obtained some of our results are sharp and respective extremal functions are mentioned.

Keywords

• Analytic function
• subordination
• Hankel
• Toeplitz and Hermitian-Toeplitz determinants
• modulo difference
• cardioid domain

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