In the present paper, we introduce new subclasses of bi-starlike and bi-convex functions complex order associated with Erdély–Kober-type integral operator in open unit disc find estimates initial coefficients these classes. Moreover, obtain Fekete-Szegő inequalities for Some significances our results are pointed out as corollaries.

Abstract The aim of this paper is to prove the theorem which generates many examples functions belonging a geometrically defined class uniformly starlike introduced by Goodman in 1991. Only very few explicit were known until now. Next we obtain inclusion relations between some subclasses convex and functions.