HANKEL DETERMINANT FOR CERTAIN CLASS OF ANALYTIC FUNCTION DEFINED BY GEBERALIZED DERIVATIVE OPERATOR

The authors in [1] have recently introduced a new generalised derivatives operator mu(lambda 1,lambda 2) (n,m) which generalised many well-known operators studied earlier by many different authors. By making use of the generalised derivative operator mu(n,m)(lambda 1,lambda 2) the authors derive the class of function denoted by H-lambda 1,lambda 2(n,m) which contain normalised analytic univalent functions f defined on the open unit disc U = {z is an element of C : vertical bar z vertical bar < 1} and satisfy Re (mu(n,m)(lambda 1,lambda 2) f(z))' > 0, (z is an element of U). This paper focuses on attaining sharp upper bound for the functional vertical bar a(2)a(4) - a(3)(2)vertical bar for functions f (z)= z + Sigma(infinity)(k=2) a(k) z(k) belonging to the class H-lambda 1,lambda 2(n,m).