An analytic function f ( z ) = z + a   n + 1   z   n + 1 + ⋯ , defined on the unit disk △ = { z : | z | < 1 } , is in the class S   p if z   f ′ ( z ) / f ( z ) is in the parabolic region |w-1|$"> Re w > | w − 1 | . This class is closely related to the class of uniformly convex functions. Sufficient conditions for function to be in S   p are obtained. In particular, we find condition on λ such that the function f ( z ) , satisfying ( 1 − α ) ( f ( z ) / z )   μ + α f ′ ( z ) ( f ( z ) / z )   μ − 1 ≺ 1 + λ z , is in S   p .