Certain properties of Bazilevic˘ type univalent class defined through subordination.

In the present paper with the aid of subordination, the authors introduce two subclasses of analytic functions denoted by S α , β (λ) (α , β , λ ∈ R , α < 1 , β > 1 , λ ≥ 0) and G (λ) defined in the open unit disk D : = { z ∈ C : | z | < 1 } . These subclasses are defined through a certain univalent function S α , β and the generating function of the Gregory coefficients G (λ) . We determine upper bounds of the initial coefficients, Fekete–Szeg o ¨ functional, Hankel determinant of second order, logarithmic coefficients and inverse coefficients of the functions belongs to these subclasses. Some of the corollaries of the main results are also pointed out. [ABSTRACT FROM AUTHOR]