Classes of (ψ, β)-differential functions of complex variable and approximation by linear averages of their Faber series - Stepanec, A.I.; Romanyuk, V.S. (Ukrains’kyi Matematychnyi Zhurnal, 1992)
We introduce the notion of (ψ, β)-derivative of a function of one complex variable, and define on the basis of this the classes L_β ^ψN (G) of (ψ, β)-differentiable analytic functions in a bounded domain G. The classes L_β ^ψN (G) consist of the Cauchy-type integrals whose densities f(ζ) are such that the induced functions f(t) on the unit circle are periodic functions of classes L_β ^ψN. We consider approximation of functions fL_β ^ψN (G) by algebraic polynomials constructed from their series expansions in Faber polynomials.