Study on Universally Prestarlike Functions of Complex Order

Abstract

Universally prestarlike functions of order \(\alpha\)\(\le\)1 in the slit domain \(\Lambda\) = \(\mathit{C}\)\[1,\(\infty\)) have been recently introduced by S. Ruscheweyh. This notion generalizes the corresponding one for functions in the unit disk \(\Delta\)( and other circular domains in C).In this paper, we introduce Universally prestarlike functions of complex order. The main objective is to give the Fekete-Szegö inequality and fractional derivative for such functions.