On certain classes of analytic functions defined by Noor integral operator

Abstract

Integral operator, introduced by Noor, is defined by using convolution. Let fn(z)=z/(1−z)n+1, n∈N0, and let f be analytic in the unit disc E. Then Inf=f(−1)n★f, where fn★f(−1)n=z/(1−z). Using this operator, certain classes of analytic functions, related with the classes of functions with bounded boundary rotation and bounded boundary radius rotation, are defined and studied in detail. Some basic properties, rate of growth of coefficients, and a radius problem are investigated. It is shown that these classes are closed under convolution with convex functions. Most of the results are best possible in some sense.