Univalent Functions with Non-Negative Coefficients involving Clausen's Hypergeometric Function

Abstract: In this work, we derived the necessary and sufficient conditions on parameters for $3F_2(^{a,b,c}{b+1,c+1};z)$ Hypergeometric Function to be in the classes $\mathcal{M}^{\ast}(\lambda,\alpha)$ and $\mathcal{N}^{\ast}(\lambda,\alpha)$ and information regarding the image of function $3F_2(^{a,b,c}{b+1,c+1};z)$ belonging to $\mathcal{R}^{\tau}(A,B)$ by applying the convolution operator in open unit disc $\mathbb{D} ={z:\, |z|<1}$.