Abstract
For a positive integer p, $A_p$ will denote the class of functions $f(z)=z^p+\sum\limits^{\infty}_{n=p+1}a_nz^n$ which are analytic in the unit disc U = {z: |z| <1}. For $0{\leq}{\alpha}{\leq}1$, 0<${\beta}{\leq}1$, $0{\leq}{\lambda}$ $S_p({\alpha},{\beta},{\lambda})$ denote the class of functions $f(z){\in}A_p$ which satisfy the condition $\left|\frac{{\frac{zf^{\prime}(z)}{f(z)}}-p}{{{\alpha}{\frac{zf^{\prime}(z)}{f(z)}}+p-{\lambda}(1+{\alpha})}}\right|$<${\beta}$ for $z{\in}U$ In this paper we obtain a representation theorem for the class $S_p({\alpha},{\beta},{\lambda})$ and also derive distortion theorem and sharp estimates for the coefficients of this class.