Universally prestarlike functions associated with generalized telephone numbers

Abstract

In this paper, we acquaint universally prestarlike generalized functions of order \(\vartheta \) with \(\vartheta \le 1\) associated with generalized telephone numbers and we get coefficient bounds for \( f\in \mathscr {R} _{\vartheta }^{u}(\Psi )\) and also for \( f^{-1} \in \mathscr {R} _{\vartheta }^{u}(\Psi )\) which has not been discussed earlier. Further we obtain the Fekete-Szegö functional for the class of universally prestarlike functions and applications to certain probability distribution based on convolution product for such functions.