Coefficient inequality for a generalized subclass of analytic functions

For α(0 ≤ α < 1), η(0 ≤ η ≤ 1), β(0 < β ≤ 1), let Hm λ,μ(α; β, η) be the class of normalised functions defined in the unit disk μ by where Dm λ,μ is a linear multiplier differential operator and g ε Pm λ,μ(α; β, η) the class of normalized functions defined in the unit disk μ by For f ε Hm λ,μ(α; β, η) and given by f(z) = z +a2z2 +a3z3 +..., a sharp upper bound is obtained for {Pipe}a3-ξa22{Pipe} when A2ξ ≥ A21 where A1 and A2 are given below.