Abstract
In this paper, the definition of g-starlike mappings of complex order γ is extended from the case of unit open disk in C to the cases of the unit ball in a complex Banach space, unit polydisk and bounded starlike circular domain in C n , respectively, where g are the Carathéodory functions and γ ∈ C ∖ { 0 } . The sharp unified solutions of Fekete–Szegö type problems for g-starlike mappings of complex order γ in several complex variables are solved. Compare with some recent corresponding works, the main results hold true without any restrictive assumptions and the proofs are also more simple. All theorems can naturally be reduced to the different cases of subclasses of starlike mappings and g-starlike mappings by choosing suitable γ and g.
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