are classes of starlike and strongly starlike functions of order β (0 < β ≤ 1), respectively. Note that S∗(β)⊂ S∗ for 0< β< 1 and S∗(1)= S∗ [5]. Kanas [2] introduced the subclass R̄δ(β) of function f ∈ S as the following. Definition 1.1. For δ ≥ 0, β ∈ (0,1], a function f normalized by (1.1) belongs to R̄δ(β) if, for z ∈D−{0} and Dδf(z)≠ 0, the following holds: ∣∣∣arg z ( Dδf(z) )′ Dδf(z) ∣∣∣≤ βπ...

By using the method of differential subordination, we obtain some sufficient conditions for strongly p-valent starlikeness.

By using the method of differential subordinations, we derive some sufficient conditions for strongly starlike functions associated with a linear operator. All these results presented here are sharp.

This article comprises the study of strongly starlike functions which are defined by using concept subordination. The function φ φ(ζ)=(1+ζ)λ, 0&lt;λ&lt;1 maps open unit disk in complex plane to a domain symmetric with respect real axis right-half plane. Using this mapping, we obtain some radius results for family functions. It is worth noting that all presented sharp.