Order of convexity of Integral Transforms and Duality

Sarika Verma, Sushma Gupta, Sukhjit Singh

Recently, Ali et al defined the class ${\mathcal{W}}_{\beta }(\alpha ,\gamma )$ consisting of functions $f$ which satisfy $$\Re e^{i\varphi }\left((1-\alpha +2\gamma )\frac{f(z)}{z}+(\alpha -2\gamma )f^{\prime }(z)+\gamma z{f}^{\prime \prime }(z)-\beta \right)>0,$$ fo…