On the order of convolution consistence of certain classes of harmonic functions with varying arguments

Making use of a modified Hadamard product or convolution of har-monic functions with varying arguments, combined with an integral operator, we study when these functions belong to a given class. Following an idea of U. Bed-narz and J. Sokol we define the order of convolution consistence of three classes of functions and determine it for certain classes of harmonic functions with varying arguments defined using a convolution operator.