Second Hankel determinant for a class of analytic functions defined by a linear operator

By making use of the linear operator $Theta _m^{lambda ,n} ,,,m in mathbb{N}={1,2,3,ldots}$ and $lambda ,,,n in mathbb{N}_0 = mathbb{N} cup { 0}$ given by the authors, a class of analytic functions $S_m^{lambda ,n}(alpha ,sigma ) ( {| alpha| < pi/2}, ; 0leq sigma <1) $ is introduced. The object of the present paper is to obtain sharp upper bound for functional $ left| {,a_2 a_4 - a_3 ^2 } ight|.$