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For $\alpha\geq 0$, $\delta>0$, $\beta<1$ and $\gamma\geq 0$, the class$\mathcal{W}_{\beta}^\delta(\alpha,\gamma)$ consist of analytic and normalizedfunctions $f$ along with the condition \begin{align*} {\rm Re\,}e^{i\phi}(\dfrac{}{}(1\!-\!\alpha\!+\!2\gamma)\!({f}/{z})^\delta+(\alpha\!-\!3\gamma\!+\!\gamma[\dfrac{}{}(1-{1}/{\delta})({zf'}/{f})+{1}/{\delta}(1+{zf''}/{f'})]).\\ .\dfrac{}{}({f}/{z})^\delta\!({zf'}/{f})-\beta)>0, \end{align*} where $\phi\in\mathbb{R}$ and $|z|<1$, istaken into consideration. The class $\mathcal{S}^\ast_s(\zeta)$ be the subclassof the univalent functions, defined by the analytic characterization ${\rmRe}{\,}({zf'}/{f})>\zeta$, for $0\leq \zeta< 1$,$0<\delta\leq\frac{1}{(1-\zeta)}$ and $|z|<1$. The admissible and sufficientconditions on $\lambda(t)$ are examined, so that the generalized and non-linearintegral transforms \begin{align*} V_{\lambda}^\delta(f)(z)= (\int_0^1\lambda(t) ({f(tz)}/{t})^\delta dt)^{1/\delta}, \end{align*} maps the functionfrom $\mathcal{W}_{\beta}^\delta(\alpha,\gamma)$ into$\mathcal{S}^\ast_s(\zeta)$. Moreover, several interesting applications forspecific choices of $\lambda(t)$ are discussed, that are related to somewell-known integral operators.

Starlikeness of the generalized integral transform using duality techniques