Gamma-Bazilevic functions related with generalized telephone numbers

The purpose of this paper is to consider coefficient estimates in a class of functions ${\mathfrak{G}}_{\vartheta }^{\kappa }(\mathcal{X},\mathrm{\varkappa })$ consisting of analytic functions $f$ normalized by $f(0)=f^{\mathrm{\prime }}(0)-1=0$\ in the open unit disk $\mathrm{\Delta }=\{z:z\in \mathbb{C}\text{and}\mid z\mid <1\}$ subordinating generalized telephone numbers, to derive certain coefficient estimates $a_2,a_3$ and Fekete-Szegö inequality for $f\in {\mathfrak{G}}_{\vartheta }^{\kappa }(\mathcal{X},\mathrm{\varkappa })$. A similar results have been done for the function $f^{-1}$ and $\log {\displaystyle \frac{f(z)}{z}}\mathrm{.}$Similarly application of our results to certain functions defined by using convolution products with a normalized analytic function is given, and in particular we state Fekete-Szeg"{o} inequalities for subclasses described through Poisson Borel and Pascal distribution series.