The Fekete-Szegö functional and the Hankel determinant for a certain class of analytic functions involving the Hohlov operator

Abstract

<abstract><p>In this paper, we introduce and study a new subclass of normalized functions that are analytic and univalent in the open unit disk $ \mathbb{U} = \{z:z\in \mathcal{C}\; \; \text{and}\; \; |z| < 1\}, $ which satisfies the following geometric criterion:</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} \Re\left(\frac{\mathcal{L}_{u, v}^{w}f(z)}{z}(1-e^{-2i\phi}\mu^2z^2)e^{i\phi}\right)>0, \end{equation*} $\end{document} </tex-math></disp-formula></p> <p>where $ z\in \mathbb{U} $, $ 0\leqq \mu\leqq 1 $ and $ \phi\in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) $, and which is associated with the Hohlov operator $ \mathcal{L}_{u, v}^{w} $. For functions in this class, the coefficient bounds, as well as upper estimates for the Fekete-Szegö functional and the Hankel determinant, are investigated.</p></abstract>

Generalized Bounded Turning Functions Connected with Gregory Coefficients

“…According to this finding, the class S * has the best upper bound on |H 3 (1)|. Fekete-Szegö problem and Hankel determinants have been discussed recently in numerous articles by Deniz and their coauthors (see, [11,16]) and Srivastava and their coauthors (see, for example, [21][22][23][24]).…”

Sharp coefficients bounds for Starlike functions associated with Gregory coefficients

“…This result the best known upper bound of |H 3 (1)| for the class S * . Recently, Hankel determinants and Fekete-Szegö problem have been considered in many papers of Srivastava and his co-authors (see, for example, [40][41][42][43][44]) and Deniz and his co-authors (see, [12,23]).…”

Certain Class of Bi-Univalent Functions Defined by Sălăgean q-Difference Operator Related with Involution Numbers

“…The study of bi-univalent functions gained momentum mainly due to the work of Srivastava et al [17]. Motivated by this, many researchers [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] (also the references cited therein) recently investigated several interesting subclasses of the class Σ and found non-sharp estimates on the first two Taylor-Maclaurin coefficients. Motivated by recent study on telephone numbers [34] and using the Sȃlȃgean q-differential operator defined by ( 5), for functions ξ of the form (7) as given in [33], we have…”