new subclasses of ozaka’s convex functions

Let s∗l (λ) and cvl (λ) be the classes of functions f, analytic in the unit disc ∆ = {z : |z| < 1}, with the normalization f( 0) = f´(0) − 1 = 0, which satisfies the conditions zf´(z)/f (z) ≺ (1 + z)λ and (1 + zf′′(z)/f′(z) ≺ (1 + z)λ (0 < λ ≤ 1), where ≺ is the subordination relation, respectively. the classes s∗l (λ) and cvl(λ) are subfamilies of the known classes of strongly starlike and convex functions of order λ. we consider the relations between s∗l (λ), cvl(λ) and other classes geometrically defined. also, we obtain the sharp radius of convexity for functions belonging to s∗l (λ) class. furthermore, the norm of pre-schwarzian derivatives and univalency of functions f which satisfy the condition ℜ {1 + zf′′(z)/f′(z)} < 1 + λ/2 (z ∈ ∆), are considered.