Partial sums of generalized Rabotnov function
Let $(\mathbb{R}_{α,β,γ}(z))_{m}(z)=z+\sum_{n=1}^{m}A_{n}z^{n+1}$ be the sequence of partial sums of the normalized Rabotnov functions $\mathbb{R}_{α,β,γ}(z)=z+\sum_{n=1}^{\infty }A_{n}z^{n+1}$ where $A_{n}=\frac{β^{n}Γ\left( γ+α\right) }{Γ\left( \left( γ+α\right) (n+1)\right) }.$ The purpose of the present paper is to determine lower bounds for $\mathfrak{R}\left \{ \frac{\mathbb{R}_{α,β,γ}(z)% }{(\mathbb{R}_{α,β,γ})_{m}(z)}\right \} ,\mathfrak{R}% \left \{ \frac{(\mathbb{R}_{α,β,γ})_{m}(z)}{\mathbb{R}% _{α,β,γ}(z)}\right \} ,$ $\mathfrak{R}\left \{ \frac{\mathbb{R}_{α,β,γ}(z)}{(\mathbb{% R}_{α,β,γ})_{m}^{\prime }(z)}\right \} ,\mathfrak{R}% \left \{ \frac{(\mathbb{R}_{α,β,γ})_{m}^{\prime }(z)}{% \mathbb{R}_{α,β,γ}(z)}\right \} .$ Furthermore, we give lower bounds for $\mathfrak{R}\left \{ \frac{\mathbb{I}\left[ \mathbb{R}% _{α,β,γ}\right] (z)}{(\mathbb{I}\left[ \mathbb{R}_{α,β,γ}\right] )_{m}(z)}\right \} $ and $\mathfrak{R}\left \{ \frac{% (\mathbb{I}\left[ \mathbb{R}_{α,β,γ}\right] )_{m}(z)}{% \mathbb{I}\left[ \mathbb{R}_{α,β,γ}\right] (z)}\right \} $ where $\mathbb{I}\left[ \mathbb{R}_{α,β,γ}\right] $ is the Alexander transform of $\mathbb{R}_{α,β,γ}$. Several examples of the main results are also considered.