Fekete–Szegö problem for Bavrin’s functions and close-to-starlike mappings in $${\mathbb {C}}^{n}

The paper is devoted to the study of a family of complex-valued holomorphic functions and a family of holomorphic mappings in $${\mathbb {C}}^{n}.$$ C n . More precisely, the article concerns a Bavrin’s family of functions defined on a bounded complete n -circular domain $${\mathcal {G}}$$ G of $${\mathbb {C}}^{n}$$ C n and a family of biholomorphic mappings on the Euclidean open unit ball in $${\mathbb {C}}^{n}.$$ C n . The presented results include some estimates of a combination of the Fréchet differentials at the point $$z=0,$$ z = 0 , of the first and second order for Bavrin’s functions, also of the second and third order for biholomorphic close-to-starlike mappings in $${\mathbb {C}}^{n},$$ C n , respectively. These bounds give a generalization of the Fekete–Szegö coefficients problem for holomorphic functions of a complex variable on the case of holomorphic functions and mappings of several variables.