The main purpose of this paper is to determine the radii of starlikeness and convexity of order \(\beta \) for three different normalizations of the extended generalized k-Bessel functions defined by \(\begin{aligned} W_{v,a,d}^{k}(z)=\sum _{m\ge 0}\frac{(-d)^{m}}{\Gamma _{k}(mk+v+\frac{a+1}{2} k)\,\Gamma (m+1)}\left( \frac{z}{2}\right) ^{2m+\frac{v}{k}}, \end{aligned}\) where \(k>0\) and \(v,a,d\in \mathbb {C}\) . Moreover, we obtain tight lower and upper bounds for the radii of starlikeness and convexity of order zero. The characterization of entire functions in the Laguerre–Polya class plays a crucial role in this paper.
