Ruscheweyh-type harmonic functions with correlated coefficients

Abstract

In the paper we introduce the classes of functions with correlated
coefficients defined by generalized Ruscheweyh derivatives. Also, motivated
by Ruscheweyh we introduce the dual set for harmonic functions and we show
that the classes of functions can be presented as dual sets. Moreover, by
using extreme points theory, we obtain estimations of classical convex
functionals on the defined classes of functions. Some applications of the
main results are also considered.