Second Hankel determinant for a subclass of analytic functions defined by S$\check{a}$l$\check{a}$gean-difference operator
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 open unit disk $\Delta=\{z \in \mathbb{C}\colon |z|<1\}$ and making use of S\v{a}l\v{a}gean-difference operator, whic...
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| Main Authors: | , |
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| Format: | Article |
| Language: | German |
| Published: |
Ivan Franko National University of Lviv
2022-06-01
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| Series: | Математичні Студії |
| Subjects: | |
| Online Access: | http://matstud.org.ua/ojs/index.php/matstud/article/view/96 |
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| Summary: | 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 open
unit 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 $\Delta$ , we
designate definite new classes of analytic functions $\mathcal{R}_{\lambda}^{\beta}(\psi)$ in $\Delta$. For functionsin this new class , significant
coefficient 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. |
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| ISSN: | 1027-4634 2411-0620 |