The Fekete-Szegö problem for starlike mappings and nonlinear resolvents of the Carathéodory family on the unit balls of complex Banach spaces

In this paper, we first give a coefficient inequality for holomorphic functions on the unit disc 𝕌 in ℂ which are subordinate to a holomorphic function p on 𝕌 with p'(0) 0 . Next, as applications of this theorem, we will give the Fekete-Szegö inequality for subclasses of normalized starlike mappings and normalized quasi-convex mappings of type B on the unit ball 𝔹 of a complex Banach space. We also give the Fekete-Szegö inequality for (1+r)J_r , where J_r=J_r[f] is the nonlinear resolvent of a mapping f in the Carathéodory family ℳ(𝔹) . Various particular cases will be also considered.