Second Hankel determinant for a subclass of analytic functions defined by S$\check{a}$l$\check{a}$gean-difference operator

Abstract

In the present investigation, inspired by the work on Yamaguchi type class of analytic functions satisfyingthe analytic criteria $\mathfrak{Re}\{\frac{f (z)}{z}\} > 0, $ in the openunit disk $\Delta=\{z \in \mathbb{C}\colon |z|<1\}$ and making use of S\v{a}l\v{a}gean-difference operator, which is a special type of Dunkl operator with Dunkl constant $\vartheta$ in $\Delta$ , wedesignate definite new classes of analytic functions $\mathcal{R}_{\lambda}^{\beta}(\psi)$ in $\Delta$. For functionsin this new class , significantcoefficient estimates $|a_2|$ and $a_3|$ are obtained. Moreover, Fekete-Szeg\H{o} inequalities and second Hankel determinant for the function belonging to this class are derived. By fixing the parameters a number of special cases are developed are new (or generalization) of the results of earlier researchers in this direction.

Results on Toeplitz Determinants for Subclasses of Analytic Functions Associated to q-Derivative Operator

“…The estimates for Toeplitz determinants T r (n) for functions in S * q and R, when n and r are small have been studied in Ali et al (2018) , Al-Khafaji et al (2020) , Al-shbeil et al (2022 , Buyankara and Çağlar (2023) , Soh et al (2021) , Radhika et al (2018) , Ramachandran and Kavitha (2017) , Ayinla and Bello (2021) , Rasheed et al (2023) , Sivasubramanian et al (2016) , Srivastava et al (2019) , Tang et al (2023) , Tang et al (2021) , Wahid et al (2022), Wanas et al (2023). Motivated by these results, this study aims to find the determinants of Toeplitz determinants T r (n) for functions in S * q and R q , when n and r are small.…”