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

Maslina Darus, Rabha W. Ibrahim

Abstract

We define a generalized differential and integral operators on the class A of
analytic functions f(z) = z +P1n=2anzn in the unit disk U:= {z2C:|z| <1} involving k−th Hadamard product (convolution) as follows Dk,f(z) = z +1X n=2 [(n − 1)( − ) + n]kanzn, (z 2 U). These operators are generalized for some of well known operators for example Sˇalˇagean operator. New classes containing these operators are investigated. Characterization and other properties of these classes are studied.

Keywords

Hadamard product; Integral operator; Differential operator; Sˇalˇagean operator

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