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