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|$" id="E5"> 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 .