A function f , analytic in the unit disc Δ , is said to be in the family R n ( α ) if {{\left( {n + \alpha } \right)} \mathord{\left/ {\vphantom {{\left( {n + \alpha } \right)} {\left( {n + 1} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {n + 1} \right)}}$"> Re { ( z n f ( z ) ) ( n + 1 ) / ( z n − 1 f ( z ) ) ( n ) } > ( n + α ) / ( n + 1 ) for some α ( 0 ≤ α < 1 ) and for all z in Δ , where n  ϵ  N o , N o = { 0 , 1 , 2 , … } . The The class R n ( α ) contains the starlike functions of order α for n ≥ 0 and the convex functions of order α for n ≥ 1 . We study a class of integral operators defined on R n ( α ) . Finally an argument theorem is proved.