In the present paper, we study functions f which are analytic and normalized in the open unit disc such that satisfy the following subordination

(zf'(z)/f(z) - 1) < (z-tz^2)/(1-z)^2, (z\in D).

Some properties of these functions including the radius of starlikeness and convexity, majoriziation problem, initial coefficient estimates, Fekete-Szegö problem and estimation of initial logarithmic coefficients and pre-Schwarzian norm are investigated.