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

T. Panigrahi; G. Murugusundaramoorthy

doi:10.30970/ms.57.2.147-156

T. Panigrahi Institute of Mathematics and Applications Andharua, Bhubaneswar Odisha, India
G. Murugusundaramoorthy Sr.Professor of Mathematics, School of Advanced Sciences, VIT UNIVERSITY, Vellore-632 014, India, www.vit.ac.in Alternate Email: gms@vit.ac.in https://orcid.org/0000-0001-8285-6619

DOI: https://doi.org/10.30970/ms.57.2.147-156

Анотація

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.

Біографії авторів

T. Panigrahi, Institute of Mathematics and Applications Andharua, Bhubaneswar Odisha, India

Institute of Mathematics and Applications Andharua, Bhubaneswar Odisha, India

G. Murugusundaramoorthy, Sr.Professor of Mathematics, School of Advanced Sciences, VIT UNIVERSITY, Vellore-632 014, India, www.vit.ac.in Alternate Email: gms@vit.ac.in

Dr.G.Murugusundaramoorthy, Ph.DSr.Professor of Mathematics,School of Advanced Sciences,VIT UNIVERSITY, Vellore-632 014.India, www.vit.ac.in. Alternate Email: gms@vit.ac.in

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