On new subclasses of analytic functions involving generalized differential and integral operators

Abstract

We define a generalized differential and integral operators on the class $frak{A}$ of analytic functions $f(z) = z + sum^{infty}_{n=2}a_nz^n$ in the unit disk $U := {z ∈ Bbb{C}:|z| < 1} involving k−th Hadamard product (convolution) as follows $D^k_{alpha,lambda}f(z)=z+sumlimits_{n=2}^{infty} [(n-1)(lambda-alpha)+n]^k a_n z^n, hspace {3mm} (z in U)$. These operators are generalized for some of well known operators for example Salagean operator. New classes containing these operators are investigated. Characterization and other properties of these classes are studied. 2000 Mathematics Subject Classifications: 30C45