Partial sums of the normalized Dini functions

Let $\left( w_{α,v}\right) _{m}(z)=z+\sum\limits_{n=1}^{m}a_{n}z^{n+1}$ be the sequence of partial sums of normalized Dini functions $w_{α,v}(z)=z+\sum\limits_{n=1}^{\infty }a_{n}z^{n+1}$ where $a_{n}=\frac{\left( -1\right) ^{n}\left( 2n+α\right) }{α4^{n}n!\left( v+1\right) _{n}% }$. The aim of the present paper is to obtain lower bounds for $\mathcal{R} \left\{ \frac{w_{α,v}(z)}{\left( w_{α,v}\right) _{m}(z)}\right\} ,$ $\mathcal{R}\left\{ \frac{\left( w_{α,v}\right) _{m}(z)}{w_{α,v}(z)}\right\} ,$ $\mathcal{R}\left\{ \frac{w_{α,v}^{^{\prime }}(z)}{ \left( w_{α,v}\right) _{m}^{^{\prime }}(z)}\right\}$ and $\mathcal{R} \left\{ \frac{\left( w_{α,v}\right) _{m}^{^{\prime }}(z)}{w_{α,v}^{^{\prime }}(z)}\right\}$ . Also we give a few geometric description regarding image domains of some functions.

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