Second Hankel determinant for a subclass of analytic functions defined by S$\check{a}$l$\check{a}$gean-difference operator - T. Panigrahi; G. Murugusundaramoorthy (Математичні Студії)
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 $Δ=\{z \in \mathbb{C}\colon |z|<1\}$ and making use of Sǎlǎgean-difference operator, which is a special type of Dunkl operator with Dunkl constant $ϑ$ in $Δ$ , we designate definite new classes of analytic functions $\mathcal{R}_{λ}^{β}(ψ)$ in $Δ$. For functionsin this new class , significant coefficient estimates $|a_2|$ and $a_3|$ are obtained. Moreover, Fekete-Szegő 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.